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Standards and
Specifications for
Geodetic Control .Networks
Federal Geodetic Control Committee
Rear Adm. John D. Bossler, Chairman
Rockville, Maryland
September 1984
FGCC
�1
Standards and Specifications
for Geodetic Control Networks
Federal Geodetic Control Committee
John D. Bossler, Chairman
September 1984
For information write:
Chairman
Federal Geodetic Control Coinmittee
6001 Executive Boulevard
Rockville, Maryland 20852
For sale by the National Geodetic Information Branch (N/CG17x2),
NOAA, Rockville, MD 20852
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,
Library of Congress Cataloging in Publication Data
United States. Federal Geodetic Control Committee.
Standard and specifications for geodetic control networks.
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Replaces both "Classification, standards .of accuracy, and general specifications
of ieodetic control surveys," issued February 1974 and "Specifications to support
classification, standards of accuracy, and general specifications of geodetic contrcii
surveys," revised June 1980 Pref.
"September 1984."
1. Geodesy-Standards-United States. I. Bossler, John D. II. Title.
QB296.U89U5 1984
526.3'3
84-600257
ii
(
Preface
This single publication is designed to replace both "Classification, Standards of Accuracy and
General Specifications of Geodetic Control Surveys," issued February 1974, and "Specifications to
Support Classification, Standards of Accuracy, and General Specifications of Geodetic Control Sur­
veys," issued June 1980. Because requirements and methods for acquisition of geodetic control are
changing rapidly, this publication is being released in loose-leaf format so that it can be updated more
conveniently and efficiently. Recipients of this publication wishing to receive updated information
should complete and mail the form below. Comments on the contents and format of the publication are
welcomed and should be addressed to:
,
FGCC Secretariat, Code N/CG1x5
National Geodetic Survey, NOAA
Rockville, Maryland 20852
c�
'·
(Detach and mail to: National Geodetic Infonnation Branch,
code N/CG17x2, NOAA, Rockville, Maryland 20852)
Please inform me of updated information for "Standards and Specifications for Geodetic Control
Networks."
Name: ---------------------------------Address: ---------------------------------
D
Check here if address given is a private residence.
(signature)
(date)
iii
Contents
,,
:-;
Preface.......................................................................................................................................... ..
iii
1. Introduction..............................................................................................................................
1-1
2 Standards .................................................................................. · .............................................
2.1 Horizontal control network standards ............................................................................
2.2 Vertical control network standards ................................................................................
2.3 Gravity control network standards.................................................................................
2-1
2-1
2-2
2-3
3. Specifications............................................................................................................................
3.1 Introduction ..................................................................................................................
3.2 Triangulation.................................................................................................................
3.3 Traverse ........................................................................................................................
3.4 Inertial surveying ..........................................................................................................
3.5 Geodetic leveling...........................................................................................................
3.6 Photogrammetry .................................................................. :........................................
3.7 Satellite Doppler positioning..........................................................................................
3.8 A bsolute gravimetry......................................................................................................
3.9 Relative gravimetry ........................ :..............................................................................
3-1
3-1
3-1
3-3
3-5
3-6
3-8
3-9
3-12
3-13-
4. Infonnation.... .............. ·...........................................................................................................
4-1
5. References ................................................................................................................................
5-1
A ppendix A. Governmental authority...................,........................................... ,...............................
A.I A uthority.....................................................................................................................
A.2 References ...................................................................................................................
A-1
A-1
A-1
A ppendix B. Variance factor estimation...........................................................................................
B.1 Introduction..................................................................................................................
B.2 Global variance factor estimation..................................................................................
B.3 Local variance factor estimation .......�...........................................................................
B.4 Iterated almost unbiased estimation ..............................................................................
B.5 References....................................................................................................................
B-1
B-1
B-2
B-2
B-3
B-4
A ppendix C. Procedures for submitting data to the National Geodetic Survey................................
C-1
V
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1. Introduction
vertical standards are defined in reasonable conformance
with past practice. The recent development of highly
accurate absolute gravity instrumentation now allows a
gravity reference standard. In the section on "Standards,"
the classification standards for each of the control net­
works are described, sample computations performed,
and monumentation requirements given.
Control networks can be produced only by making very
accurate measurements which are referred to identifiable
control points. The combination of survey design, instru­
mentation, calibration procedures, observational techniques,
and data reduction methods is known as a measurement
system. The section on "Specifications" describes impor­
tant components and states permissible tolerances for a
variety of measurement systems.
Clearly, the control networks would be of little use if
the datum values were not published. The section entitled
"Information" describes the various products and for­
mats of available geodetic data.
Upon request, the National Geodetic Survey will accept
data submitted in the correct formats with the proper
supporting documentation (appendix C) for incorpora­
tion into the national networks. When a survey is submit­
ted for inclusion into the national networks, the survey
measurements are processed in a quality control proce­
dure that leads to their classification of accuracy and
storage in the National Geodetic Survey data base. To
fully explain the process we shall trace a survey from the
planning stage to admission into the data base. This example
will provide an overview of the standards and specifica­
tions, and how they work together.
The user should first compare the distribution and
accuracy of current geodetic control with both' immediate
and long-term needs. From this basis, requirements for
the extent and accuracy of the planned survey are deter­
mined. The classification standards of the control net­
works will help in this formulation. Hereafter, the require­
ments for the accuracy of the planned survey will be
referred to as the "intended accuracy" of the survey. A
measurement system is then chosen, based on various
factors such as: distribution and accuracy of present con­
trol; region of the country; extent, distribution, and accu­
racy of the desired control; terrain and accessibility of
control; and economic factors.
Upon selection of the measurement system, a survey
design can be started. The design will be strongly depen-
The Government of the United States makes nation­
wide surveys, maps, and charts of various kinds. These are
necessary to support the conduct of public business at all
levels of government, for planning and carrying out nationai.
and local projects, the development and utilization of
natural resources, national defense, land management,
and monitoring crustal motion. Requirements for geo­
detic control surveys are most critical where intense devel­
opment is taking place, particularly offshore areas, where
surveys are used in the exploration and development of
natural resources, and in delineation of state and interna­
tional boundaries.
State and local governments and industry regularly
cooperate in various parts of the total surveying and
mapping program. In surveying and mapping large areas:
it is first necessary to establish frameworks· of horizontal,
vertical, and gravity control. These provide a common
basis for all surveying and mapping operations to ensure a
coherent product. A reference system, or datum, is the set
of numerical quantities that serves as a common basis.
Three National Geodetic Control Networks have been
created by the Government to provide the datums. It is
the responsibility of the National Geodetic Survey (NGS) to
actively maintain the National Geodetic Control Net­
works (appendix A).
These control networks consist of stable, identifiable
points tied together by extremely accurate observations.
From these observations, datum values (coordinates or
gravity) are computed and published. These datum values
provide the common basis that is so important to survey­
ing and mapping activities.
As stated, the United States maintains three control
networks. A horizontal network provides geodetic lati­
tudes and longitudes in the North American Datum ref­
erence system; a vertical network furnishes elevations in
the National Geodetic Vertical Datum reference system;
and a gravity network supplies gravity values in the U.S.
absolute gravity reference system. A given station may be
a control point in one, two, or all three control networks.
It is not feasible for all points in the control networks to
be of the highest possible accuracy. Different levels of
accuracy are referred to as the "order" of a point. Orders
a,re often subdivided farther b y a "class" dt;signation,
Datum values for a station are assigned an order (and
class) based upon the appropriate classification standard
for each of the three control networks. Horizontal and
1-1
0
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procedure to make sure that all users may place confi­
dence in the new survey points. First, the data and docu­
mentation are examined for compliance with the mea­
surement system specifications for the intended accuracy
of the new survey. Then office computations are performed,
including a minimally constrained least squares adjust­
ment. (See appendix B for details.) From this adjustment,
accuracy measures can be computed by error propaga­
tion. The accuracy classification thus computed is called
the "provisional accuracy" of the survey.
The provisional accuracy is compared to the intended
accuracy. The difference indicates the departure of the
accuracy of the survey from the specifications. If the
difference is small, the intended accuracy has precedence
because a possible shift in classification is not warranted.
However, if the difference is substantial, the provisional
accuracy will supersede the intended accuracy, either as a
downgrade or an upgrade.
As the final step in the quality control procedure, the
variance factor ratio computation using established con­
trol, as explained in the section on "Standards," is deter­
mined for the new survey. If this result meets the criteria
stated there, then the survey is classified in accordance
with the provisional accuracy (or intended accuracy, whichever has precedence).
Cases arise where the variance factor ratio is signifi­
cantly larger than expected. Then the control network is
at fault, or the new survey is subject to some unmodeled
error source which degrades its accuracy. Both the estab­
lished control measurements and the new survey mea­
surements will be scrutinized by NGS to determine the
source of the problem. In difficult cases, NGS may make
diagnostic measurements in the field.
Upon completion of the quality control check, the sur­
vey measurements and datum values are placed into the
data base. They become immediately available for elec­
tronic retrieval, and will be distributed in the next publi­
cation cycle by the National Geodetic Information Branch of
NGS.
A final remark bears on the relationship between the
classification standards and measurement system speci­
fications. Specifications are combinations of rules of thumb
and studies of error propagation, based upon experience,
of how to best achieve a desired level of quality. Unfortu­
nately, there is no guarantee that a particular standard
will be met if the associated specifications are followed.
However, the situation is ameliorated by a safety factor of
two incorporated in the standards and specifications.
Because of this safety factor, it is possible that one may
fail to meet the specifications and still satisfy the desired
standard. This is why the geodetic control is not automat­
ically downgraded when one does not adhere to the speci­
fications. Slight departures from the specifications can be
accommodated. In practice, one should always strive to
meet the measurement system specifications when extending
a National Geodetic Control Network.
dent upon the "Network Geometry" specifications for
that measurement system. Of particular importance is the
requirement to connect to previously established control
points. If this is not done, then the survey cannot be placed
on the national datum. An adequate number of existing
control point connections are often required in the speci­
fications in order to ensure strong network geometry for
other users of the control, and to provide several closure
checks to help measure accuracy. NGS can certify the
results of a survey only if it is connected to the national
network.
Situations will arise where one cannot, or prefers not to,
conform to the specifications. NGS may downgrade the
classification of a survey based upon failup; to adhere to
the measurement system specifications if the departure
degrades the precision, accuracy, or utility of the survey.
On the other hand, if specification requirements for the
desired level of accuracy are exceeded, it may be possible
to upgrade a survey to a higher classification.
Depending upon circumstances, one may wish to go
into the field to recover old control and perform recon­
naissance and site inspection for the new survey. Monu­
mentation may be performed at this stage. Instruments
should be checked to conform to the "Instrumentation"
specifications, and to meet the "Calibration Procedures"
specifications. Frequent calibration is an excellent method to
help ensure accurate surveys.
In the field, the "Field Procedures" specifications are
used to guide the methods for taking survey measure­
ments. It must be stressed that the "Field Procedures"
section is not an exhaustive account of how to perform
observations. Reference should be made also to the appropri­
ate manuals of observation methods and instruments.
Computational checks can be found in the "Field Pro­
cedures" as well as in the "Office Procedures" specifica­
tions, since one will probably want to perform some of the
computations in the field to detect blunders. It is not
necessary for the user to do the computations described in
the "Office Procedures" specifications, since they will be
done by NGS. However, it is certainly in the interest of
the user to compute these checks before leaving the field,
in case reobservations are necessary. With the tremen­
dous increase in programmable calculator and small com­
puter technology, any of the computations in the "Office
Procedures" specifications could be done with ease in the
field.
At this point the survey measurements have been col­
lected, together with the new description and recovery
notes of the stations in the new survey. They are then
placed into the formats specified in the Federal Geodetic
Control Committee (FGCC) publications Input Formats
and Specifications of the National Geodetic Survey Data
Base. Further details of this process can be found in
appendix C, "Procedures for Submitting Data to the
National Geodetic Survey."
The data and supporting documentation, after being
received at NGS, are processed through a quality control
1-2
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,
2. Standards
relation of specific accuracy to the coordinates of all other
points in the horizontal control network. This relation is
expressed as a distance accuracy, 1:a. A distance accu­
racy is the ratio of the relative positional error of a pair of
control points to the horizontal separation of those points.
· The classification standards of the National Geodetic
ControlNetworks are based on accuracy. This means that
when control points in a particular survey are classified,
. they are certified as having datum values consistent with
all other points in the network, not merely those within
that particular survey. It is not observation closures within a
survey which are used to classify control points, but the
ability of that survey to duplicate already established
control values. This comparison takes into account mod­
els of crustal motion, refraction, and any other systematic
effects known to influence the survey measurements.
The NGS procedure leading to classification covers
four steps:
1. The survey measurements, field records, sketches,
and other documentation are examined to verify
compliance with the specifications for the intended
accuracy of the survey. This examination may lead
to a modification of the intended accuracy.
2. Results of a minimally constrained least squares
adjustment of the survey measurements are exam­
ined to ensure correct weighting of the observations
and freedom from blunders.
3. Accuracy measures computed by random error propa­
gation determine the provisional accuracy. If the
provisional accuracy is substantially different from
the intended accuracy of the survey, then the provi­
sional accuracy supersedes the intended accuracy.
4. A variance factor ratio for the new survey combined
with network data is computed by the Iterated Almost
Unbiased Estimator (!AUE) method (appendix B).
If the variance factor ratio is reasonably close to 1.0
(typically less than 1.5), then the survey is consid­
ered to check with the network, and the survey is
classified with the provisional (or intended) accura­
cy. If the variance factor ratio is much greater than
1.0 (typically 1.5 or greater), then the survey is con­
sidered to not check with the network, and both the
survey and network measurements will be scruti­
nized for the source of the problem.
Table 2.1-Distance accuracy standards
Minimum
distance accuracy
Classification
First-order ....................................................
Second-order, class I ....................................
Second-order, class II ...................................
Third-order, class I ......................................
Third-order, class II .....................................
1:100,000
1: 50,000
1: 20,000
1: 10,000
1: 5,000
A distance accuracy, 1:a, is computed from a mini­
mally constrained, correctly weighted, least squares adjust­
ment by:
a = d/s
where
a=distance accuracy denominator
s = propagated standard deviation of distance between
survey points obtained from the least squares adjust­
ment
d=distance between survey points
The distance accuracy pertains to all pairs of points
(but in practice is computed for a sampling of pairs of
points). The worst distance accuracy (smallest denominator)
is taken as the provisional accuracy. If this is substan­
tially large� or smaller than the intended accuracy, then
the provisional accuracy takes precedence.
As a test for systematic errors, the variance factor ratio
of the new survey is computed by the Iterated Almost
Unbiased Estimator (IAUE) method described in appen­
dix B. This computation combines the new survey mea­
surements with existing network data, which are assumed
to be correctly weighted and free of systematic error. If
the variance factor ratio is substantially greater than
unity then the survey does not . check with the network,
and both the survey and the network data will be exam­
ined byNGS.
2.1 Horizontal Control Network Standards
When a horizontal control point is classified with a
particular order and· class, NGS certifies that the geo­
detic latitude and longitude of that control point bear a
2-l
horizontal location which can be defined as a point. A 30centimeter-long wooden stake driven into the ground, for
example, would lack both permanence and horizontal
stability. A mountain peak is difficult to define as a point.
Typically, corrosion resistant metal disks set in a large
concrete mass have the necessary qualities. First-order
and second-order, class I, control points should have an
underground mark, at least two monumented reference
marks at right angles to one another, and at least one
monumented azimuth mark no less than 400 m from the
control point. Replacement of a temporary mark by a
more permanent mark is not acceptable unless the two
marks are connected in timely fashion by survey observations
of sufficient accuracy. Detailed information may be found in
C&GS Special Publication 247, "Manual of geodetic
triangulation."
Computer simulations performed by 'NGS have shown
that a variance factor ratio greater than ·1;5 typically
indicates systematic errors between the survey and the
network. Setting a cutoff value higher than this could
allow undetected systematic error to propagate into the
national network. On the other hand, a higher cutoff value
might be considered if the survey has only a small number
of connections to th� network, because this circumstance
would tend to increase the variance factor ratio.
In some situations, a survey has been designed in which
different sections provide different orders of control. For
these multi-order surveys, the computed distance accu­
racy denominators should be grouped into sets appropri­
ate to the different parts of the survey. Then, the smallest
value of a in each set is used to classify the control points
of· that portion, as discussed above. If there are sufficient
connections to the network, several: variance factor ratios,
one for each section of the survey, should be computed.
2.2 Vertical Control Network Standards
Horizontal Example
Suppose a survey with an intended accuracy of first­
order (1:100,000) has been performed. A series of propa­
gated distance accuracies from a minimally
· constrained
·
adjustment is now computed.
line
s
(m)
d
(m)
J:a
1-2 .......................
1-3 ...: ...: .............
2-3 .......................
0.141
0.170
0;164
17,107
20,123
• 15,505
1:121,326
1:118,371
1: 94,543
When a vertical control point is classified with a particular
order arid class, NGS certifies that the orthometric elevation
at that point bears a relation of specific accuracy to the
elevations of all other points in the vertical control net­
work. That relati9n is expressed as an elevation difference
accuracy, b. An elevation difference accuracy· is the rela­
tive elevation ·error between a pair of control points that is
scaled by the square root of their horizontal separation
traced along existing level routes.
Table 2.2-Elevation accuracy standards
Maximum elevation
difference accuracy
Classification
First-<irder, class I ........................................
First-<irder, class II.......................................
Second-<irder, class I ....................................
Second-<irder, class II...................................
Third-<irder .........................................._........
Suppose that the worst distance accuracy is 1:94,543.
This is not substantially different from the intended accuracy
of 1:100,000, which would therefore have precedence for
classification. It is not· feasible to precisely quantify
"substantially different." Judgment · and experience are
determining factors.
Now assume that a solution combining survey and
network data has been obtained (as per appendix B), and
that a variance factor ratio of 1.2 was computed for the
survey. This would be reasonably close to unity, and would
indicate that the survey checks with the network. The
survey would then be clas�ified as first-order using the
intended accuracy of 1:100,000.
However, if a variance factor of, say, 1.9 was computed,
the survey would not check with the network. Both the
survey and network measurements then would have to be
scrutinized to find the problem.
0.5
0.7
1.0
1.3
2.0
An elevation difference accuracy, b, is computed from
a minimally constrained, correctly weighted, least squares
adjustment by
b = S/yd
where
d=approximate horizontal distance in kilometers between
control point positions traced along existing level routes.
S=propagated standard deviation of elevation difference
in millimeters between survey control points obtained
from the least squares adjustment. Note that the units
of b are (mm)/ y (km).
Monumentation
Control points should be part of the National Geocletic
Horizontal Network only if they possess permanence,
horizontal stability with respect to the Earth's crust, and a
The eievation difference accuracy pertains to ,all pairs
of points (but in practice is computed for a sample). The
worst elevation difference accuracy (largest value) is taken
2-2
(
as the provisional accuracy. If this is substantially larger
or smaller than the intended accuracy, then the provi­
sional accuracy takes precedence.
As a test for systematic errors, the variance factor ratio
of the new survey is computed by the Iterated Almost
Unbiased Estimator (IAUE) method described in appen­
dix B. This computation combines the new survey mea­
surements with existing network data, which are assumed
to be correctly weighted and free of systematic error. If
the variance factor ratio is substantially greater than
unity, then the survey does not check with the network,
and both the survey and the network data will be examined byNGS.
Computer simulations performed by NGS have shown
that a variance factor ratio greater than 1.5 typically
indicates systematic errors between the survey and the
network. Setting a cutoff value higher than this. could
allow undetected systematic error to propagate into the
national network. On the other hand, a higher cutoff value•
might be considered if the survey has only a small number
of connections to the network, because this circumstance
would tend to increase the variance factor ratio.
. In some situations, a survey has been designed in which
different sections provide different orders of control. For
these multi-order surveys, the computed elevation . difference
accuracies should be grouped into sets appropriate to the
different parts of the survey. Then, the largest vaiue of b
in each set is used to classify the control points of that
portion, as discussed above. If there are sufficient connec­
tions to the network, several variance factor ratios, one for
each section of the survey, should be computed.
Vertical Example
Suppose a survey with an intended accuracy of second­
order, class II has been performed. A series of propagated
elevation difference accuracies from a minimally con­
strained adjustment is now computed.
that a variance factor ratio of 1.2 was computed for the
survey. This would be reasonably close to unity and would
indicate that the survey checks with the network. The
survey would then be classified as second-order, class II,
using the intended accuracy of 1.3.
However, if a survey variance factor ratio of, say, 1.9
was computed, the survey would not check with the net­
work. Both the survey and network measurements then
would have to be scrutinized to find the problem.
Monwnentation
Control points should be part of the National Geodetic
Vertical Network only if they possess permanence, verti­
cal stability with respect to the Earth's crust, and a verti­
cal location that can be defined as a point. A 30-centime­
ter-long wooden stake driven into the ground, for example,
would lack both permanence and vertical stability. A
rooftop lacks' stability and is difficult to define as a point.
Typically, corrosion resistant metal disks set in large rock
outcrops or long metal rods driven deep into the ground
have the necessary qualities. Replacement of a temporary
.mark by a more permanent mark is not acceptable unless
the two marks are connected in timely fashion by survey
observations of sufficient accuracy. Detailed information
may be found in NOAA Manual NOS NGS 1, "Geodetic
bench marks."
2.3 Gravity Control Network Standards
When a gravity control point is classified with a particular
order and class, NGS certifies that the gravity value at
that control point possesses a specific accuracy.
Gravity is commonly expressed in units of milligals
(mGal) or microgals (µGal) equal, respectively, to (10-5)
meters/sec2, and (10-s) meters/sec2• Classification order
refers to measurement accuracies and class to site stabili­
ty.
Table 2.3-Gravity accuracy standards
s
line
(mm)
d
(km)
b
(mm)/y (km)
1-2 .......................
1-3 .......................
2-3 .......................
1.574
1.743
2.647
1.718
2.321
4.039
1.20
1.14
1.32
Classification
Gravity accuracy
(µ.Gal)
First-order, class
· I ........................................ 20 (subject to stability
verification)
First-order, class II .................. ..................... 20
Second-order ................................................ 50
Third-order ......:...............................::..........100
When a survey establishes only new points, and where
only absolute measurements are observed, then each sur­
vey point is classified independently. The standard devia­
tion from the mean of measurements observed at that
point is corrected by the error budget for noise sources in
accordance with the following formula:
Suppose that the worst elevation difference accuracy is
1.32. This is not substantially different from the intended
accuracy of 1.3 which would therefore have precedence
for classification. It is not feasible to precisely quantify
"substantially different." Judgment and experience
are
··
determining factors.
Nowiassume that a solution combining survey and
network data has been obtained (as per appendix B), and
2-3
r- -c1 p.
Gravity Examples
Example A. Suppose a gravity survey using absolute
measurement techniques has been perfonned. These points
are then unrelated. Consider one of these survey points.
where
c =gravity accuracy
Xi =:=gravity measurement
=number of measurements
n
xm = (}; x.)/n
Assume n = 750
e=external random error
750
t=l
t
(
� (x. - xm ) 2 = .169 mGal2
The value obtained for c is then compared directly against
the gravity accuracy standards table.
When a survey establishes points at which both abso­
lute and relative measurements are made, the absolute
determination ordinarily takes precedence and the point
is classified accordingly. (However, see Example D below
for an exception.)
When a survey establishes points where only relative
measurements are observed, and where the survey is tied .
to the National Geodetic Gravity Network, then the gravity
accuracy is identified with the propagated gravity stan­
dard deviation from a minimally constrained, correctly
weighted, least squares adjustment.
The worst gravity accuracy of all the points in the
survey
is taken· as the . provisional accuracy. If the provi­
t
sional accuracy exceeds the gravity accuracy- limit set for
the intended survey clru;sification, then the survey is clas­
sified using the provisional accuracy.
As a test for systematic errors, the variance factor ratio
�of the new survey is computed by the_ Iterated Almost
--.__../'Unbiased Estimator (IAUE) method described in appen­
dix B. This computation combines the new survey measurements with existing network data which are assumed
to be correctly weighted and free of systematic error. If
the variance factor ratio is substantially greater than
unity, then the survey does not check with the network,
and both the survey and the network data will be exam­
ined byNGS.
Computer simulations performed by NGS have shown
that a variance factor ratio greater than 1.5 typically
indicates systematic errors between the survey and the
network. Setting a cutoff value higher than this could
allow undetected systematic error to propagate into the
national network. On the other hand, a higher cutoff value
might be considered if the survey has only a minimal
number of connections to the network, because this cir­
cumstance wouid tend to increase the variance factor
ratio.
In 'some situations, a survey has been designed in which
different sections provide different orders of control. For
these multi-order surveys, the computed gravity accura­
cies should be grouped into sets appropriate to the differ­
ent parts of the survey. Then, the largest value of c in each
set is used to classify the control points of that portion,. as
discussed above. If there are sufficient connections to the
._
_
/rt
etwork, several variance factor ratios, one for each part
G
of the survey, should be computed.
i= l
I
e = 5 µGal
c2 =
+ (.005)2
0.169
750-1
c = 16 µGal
The point is then classified as first-order, class II.
Example B. Suppose a relative gravity survey with an
intended accuracy of second-order (50 µGal) has been per­
fonned. A series of propagated gravity accuracies from a
minimally constrained adjustment is now computed.
Station
1
2
3
,.
Gravity standard
deviation (µGal)
38
44
55
C
r
2-4
Suppose that the worst gravity accuracy was 55 µGal.
This is worse than the intended accuracy of 50 µGal.
Therefore, the provisional accuracy of 55 µGal would
have precedence for classification, which would be set to
third-order.
Now assume that a solution combining survey and
network data has been obtained (as per appendix. B) and
that a variance factor of 1.2 was computed for the survey.
This would be· reasonably close to unity, and would indi­
cate that the survey checks with the network. The survey
would then be classified as third-order using the provi­
sional accuracy of 55 µGal.
However, if a variance factor of, say, 1.9 was computed,
the survey· would not check with the network. Both the
survey and network measurements then would have to be
scrutinized to find the problem.
Example C. Suppose a survey consisting of both abso­
lute and relative measurements has been made at the
same points. Assume the absolute observation at one of
the points yielded a classification of first-order, class II,
whereas the relative measurements produced a value to
second-order standards. The point in question would be
classified as first-order, class II, in accordance with the
absolute observation.
Example D. Suppose we have a survey similar to Case
C, where the absolute measurements at a particular point
(
checked at least twice for the first year to ensure stability.
For first-order, class II stations, the platform should be
located in an extremely stable environment, such as the
concrete floor of a mature structure. For second and
third-order stations, standard bench mark monumentation is
adequate. Replacement of a temporary mark by a more
permanent mark is not acceptable unless the two marks
are connected in timely fashion by survey observations of
sufficient accuracy. Detailed information is given in NOAA
Manual NOS NGS 1, "Geodetic bench marks." Monu­
ments should not be near sources of electromagnetic
interference.
It is recommended, but not necessary, to monument
third-order stations. However, the location associated
with the. gravity value should be recoverable, based upon
the station description.
yielded a third-order classification due to an unusually
noisy observation session, but the relative measurements
still satisfied the ·second-order standard. The point in
question would be classified as second-order, in accor­
dance with the relative measurements.
Monument.ation
Control points should be part of the National Geodetic
Grayity Network only if they possess permanence, hori­
zontal and vertical stability with respect to the Earth's
crust, and a horizontal and vertical location which can be
defined as a point. For all orders of accuracy, the mark
should be imbedded in a stable platform such as flat,
horizontal concrete. For first-order, class I stations, the
platform should be imbedded in stable, hard rock, and
,· r
/,,-
___)
\._)
2-5
l . --- ---- -- -
3. Specifications
3.1 Introduction.
performed by NGS will use models of error sources, such
as crustal motion, when they are judged to be significant
to the level of -accuracy of the survey.
All measurement systems regardless of their nature
have certain common qualities. Because of this, the mea­
surement system specifications follow a prescribed struc­
ture as outlined below. These specifications describe the
important components and state permissible tolerances
used in a general context of accurate surveying methods.
The user is cautioned that these specifications are not
substitutes for manuals that detail recommended field
operations and procedures.
The observations will have spatial or temporal relation­
ships with one another as given in the "Network Geome­
try" section. In addition, this section specifies the fre­
quency of incorporation of old control into the survey.
Computer simulations could be performed instead of fol­
lowing the "Network Geometry" and "Field Procedures"
specifications. However, the user should consult the National
Geodetic Survey before undertaking such a departure
from the specifications:
The "Instrumentation" section describes the types and
characteristics of the instruments used to make observations.·
An instrument must be able to attain the precision require­
ments given in "Field Procedures."
The section "Calibration Procedures" specifies the nature
and frequency of instrument calibration. An instrument
• must be calibrated whenever it has been damaged or
repaired.
The "Field Procedures" section specifies particular rules
and limits to be met while following an appropriate method of
ob�ervation. For a detailed account of how to perform
observations, the user should consult the appropriate
manuals.
Since NGS will perform _the computations described
under "Office Procedures," it is not necessary for the user
to do them. However, these computations provide valu. able checks on the survey measurements that could indi­
cate the need for some reobservations. This section speci­
fies commonly applied corrections to observations, and
computations which ·'monitor the precision and accuracy
of the survey. It also discusses the correctly weighted,
minimally constrained least squares adjustment used to
ensure that the survey work is free from blunders and able
to achieve the intended accuracy. Results of the least
squares adjustment are used in the quality control and
accuracy classification procedures. The adjustment
3.2 Triangulation
Triangulation is a measurement system comprised of
joined or overlapping triangles of angular observations
supported by occasional distance and astronomic obser­
vations. Triangulation is used to extend horizontal control
Network Geometry
Order
Class
First
Station spacing not less
than (km) ....................... 15
Average minimwn distance
anglet of figures not
less than ......................... 40°
Minimum distance anglet
of all figures not
less than ......................... 30°
Base line spacing not
more than (triangles)...... 5 ,
Astronomic azimuth
spacing not more
than (triangles)............... 8
Second
I
Second
II
Third Third
I
II
10
5
0.5
0.5
30°
30°
25 °
25 °
20°
20°
10
12
15
15
10
10
12
15
t Distance angle is angle opposite the side through which distance is propagated.
The new survey is required to tie to at least four net­
work control points spaced well apart. These network
points must have datum values equivalent to or better
than the intended order (and class) of the new survey. For
example, in an arc of triangulation, at least two network
control points should be occupied at each end of the arc.
Whenever the distance between two new unconnected
survey pomts is less than 20 percent of the distance between
those points traced along existing or new connections,
then a direct connection should be made between those
two survey points. In addition, the survey should tie into
any sufficiently accurate network control points within
the station .spacing distance of the survey. These network
stations should be occupied and sufficient observations
taken to make these stations integral parts -of the survey.
Nonredundant geodetic connections to the network sta­
tions are not considered sufficient ties. Nonredundantly
3-1
determined stations are not allowed. Control stations should
not be determined by intersection or resection methods;
i Simultaneous reciprocal vertical angles or geodetic level� ing are observed along base lines. A base line need not be
observed if other base lines of sufficient accuracy were
observed within the base line spacing sp,ecification in the
network, and similarly for astronomic azimuths.
CL
Order
Class
Standard deviation of
mean not to exceed ........ 0.4"
Rejection limit from
the mean ........................ 4"
Order
Class
First
Theodolite, least count ....... 0.2 !'
Second
I
Second
II
Third Third
II
I
0.2"
1.0"
1.0"
Number of independent
observations
direct/reverse ................ 3
Maximum spread ............... 10"
Maximum time interval
between reciprocal
angles (hr) ..................·....
Astronomic Azimuths
Second
II
Third Third
II
I
0.5''
0.8"
1.2"
2.0"
4"
5"
5"
5"
3
2
10"
2
10"
�"
4
Electro-Optical Distances
Minimum number of days ..
Minimum number of
measurements/day .;......
Minimum number of concentric observations/
measurement .................
Minimum number of offset
observations/
measurement .................
Maximum difference from
mean of observations
(mm) .............................
Minimum number of
readings/observation
(or equivalent) ................
Maximum difference from
mean of readings (mm) ..
1.0"
Calibration Procedures
Each year and whenever the difference between direct
and reverse readings of the theodolite depart from 180 •
by more than 30", the instrument should be adjusted
�.J for collimation error. Readjustment of the cross hairs
and the level bubble -should be done whenever their misadjustments affect the instrument reading by the amount
of the least count.
All EDM devices and retroreflectors should be serviced
regularly and checked frequently over lines of known
distances. The National Geodetic Survey has established
specific calibration base lines for this purpose. EDM
instruments should be calibrated annually, and frequency
checks made semiannually.
Infrared Di,stances
Minimum number of days ..
Minimum number of
measurements ................
Minimum number of concentric observations/
measurement .................
Minimum number of offset
observations/
measurement .................
Maximum difference from
mean of observations
(mm) .............................
Minimum number of
readings/observation
(or equivalent) ................
Maximum difference from
mean of readings (mm) ..
Field Procedures
Theodolite observations for first-order and second-order,
class I surveys may only be made at night. Reciprocal
vertical angles should be observed at times of best atmospheric conditions (between noon and late afternoon) for
all orders of accuracy. Electronic distance measurements
need a record at both ends of the line of wet and dry bulb
temperatures to ± 1 · C, and barometric pressure to ± 5
mm of mercury. The theodolite and targets should be
centered to within 1 mm over the survey mark or eccentric
point.
10"
(:
2
1
16
2
16
1
8
I
1
0.45"
0.6"
1.0"
1.7''
5"
5"
6"
6"
2*
2•
1
1
2§
2§
2§
1
2
2
2
2
2
40
40
50
60
60
10
10
10
10
10
:j:
:j:
:j:
:j:
:j:
Observations per night ........ 16
Number of nights .............. . 2
Standard deviation of
mean not to exceed ........ 0.45"
Rejection limit from
the mean ........................ 5"
c)
.::
Second
I
Reciprocal Vertical Angles
(along distance sight path)
Instrumentation
Only properly maintained theodolites are adequate for
observing directions and azimuths for triangulation. Only
precisely marked targets, mounted stably op. tripods or
supported towers, should be employed. The target should
have a clearly defined center, resolvable at the minimum
control spacing. Optical plummets or collimators are
required to ensure that the theodolites and targets are
centered over the marks. Microwave-type electronic distance measurement (EDM) equipment is not sufficiently
accurate for measuring higher-order base lines.
::
First
2*
2§
(
1
2§
2
5
5
10
10
10
10
10
10
:j:
:j:
:j:
:j:
Microwave Distances
Order
(�\ Class
First
)
G- Directions
Number ofpositions .......... 16
Second
I
Second
II
16
8 or 12t
Minimum number of
measurements ................
Minimum time span
between measurements
(hr) ................................
Third Third
. II
I
4
2
3-2
\
8
C\,-----,
/_,,,,(
l,
"-j
j
Order
Class
First
Second
I
Second
II
Maximum difference
between measurements
(mm) .............................
Minimum number of con­
centric observations/
measurement .................
Maximum difference from
mean of observations
(mm) .............................
Minimum number of
readings/observation
(or equivalent) ................
Maximum difference from
mean of readings (mm) ..
arc correction
geoid height correction
second velocity correction
crustal motion
Third Third
I
II
100
3.3 Traverse
Traverse is a measurement system comprised of joined
distance and theodolite observations supported by occasional
astronomic observations. Traverse is used to densify horizontal control.
2**
1**
100
150
20
20
Network Geometry
+
+
Order
Class
t 8 if 0.2", 12 if 1.0" resolution.
* two or more instruments.
§ one measurement at each end of the line.
i as specified by manufacturer.
•• carried out at both ends of the line.
Station spacing not less
than (km) ............................... 10
Maximum deviation of
main traverse from
straight line ............................ 20°
Minimum number of
bench mark ties ....................... 2
Bench mark tie spacing
not more than
(segments) ..........., .................. 6
Astronomic azimuth
spacing not more than
(segments) .............................. 6
Minimum number of
network control points ............. 4
Measurements of astronomic latitude and longitude
are not required in the United States, except perhaps for
first-0rder work, because sufficient information for deter­
mining deflections of the vertical exists. Detailed proce­
dures can be found in Hoskinson and Duerksen (1952).
Office Procedures
Order
Class
First
Triangle Oosure
Average not to exceed ........ LO"
Maximum not to exceed .... 3"
Second
I
Second
II
1.2"
3"
2.0"
5"
3.0"
5"
5.0"
10"
Third Third
I
II
0.4"
0.6"
0.8"
2.0"
4
2
0.5
0.5
20°
25°
30 °
40 °
2
2
2
2
8
10
15
20
12
20
25
40
3
2
2
2
The new survey is required to tie to a minimum number
of network control points spaced well apart. These net­
work points must have datum values equivalent tp or
better than the· intended order (and class) of the new
survey. Whenever the distance between two new uncon­
nected survey points is less than 20 percent of the distance
between those points traced along existing or new connec­
tions, then a direct connection must be made between
those two survey points. In addition, the survey should tie
into any sufficiently accurate network control points within
the station spacing distance of the survey. These ties must
include EDM or taped distances. Nonredundant geodetic
connections to the network stations are not considered
sufficient ties. Nonredundantly determined stations are
not allowed. Reciprocal vertical angles or geodetic level­
ing are observed along all traverse lines.
Side Checks
Mean absolute correction
by side equation not
to exceed ........................ 0.3"
First Second Second Third Third
I
II
I
II
A minimally constrained least squares adjustment will
be checked for blunders by examining the normalized
residuals. The observation weights will be checked by
inspecting the postadjustment estimate of the variance of
unit weight. Distance standard errors · computed by error
propagation in this correctly weighted least squares adjust­
ment will indicate the provisional accuracy classification.
A survey variance factor ratio will be computed to check
for systematic error. The least squares. adjustment will
use models which acC?unt for the following:
Instrumentation
Only properly maintained theodolites are adequate for
observing directions and azimuths for traverse. Only pre­
cisely marked targets, mounted stably on tripods or sup­
ported towers, should be employed. The target should
have a clearly defined center, resolvable at the minimum
control spacing. Optical plummets or collimators are
required to ensure that the theodolites and targets are
centered over the marks. Microwave0type electronic dis­
tance measurement equipment is not sufficiently accu­
rate for J?easuring first-order traverses.
semimajor axis of the ellipsoid .................................(a = 6378137 m)
reciprocal flattening of the ellipsoid .........................(1 /f = 298.257222)"
mark elevation above mean sea level........................(known to ± 1 m)
geoid heights ...........................................................(known to ± 6 m)
deflections of the vertical ........................................(known to ± 3")
geodesic correction
skew normal correction
height of instrument
height of target
sea level correction
3-3
,�
1
' ,-
1
'-,,
(�/
Order
Class
Theod o1·1te, I east count ................ 0.2"
1.0"
1.0"
1.0"
1.0"
--------------------Calibration Procedures
Each year and whenever the difference between direct
and reverse readings of the theodolite depart from 180 •
by more than 30", the instrument should be adjusted for
collimation error. Readjustment of the cross hairs and the
level bubble should be done whenever their misadjustments
affect the instrument reading by the amount of the least
count.
All electronic distance measuring devices and retroreflectors should be serviced regularly and checked fre­
quently over lines of known distances. The National Geo­
detic Survey has established specific. calibration base
lines for this purpose. EDM instruments should be cali­
brated annually, and frequency checks made semiannually.
r/-)
Minimum number of
measurciments .........................
Minimum number of concentric
observations/measurement......
Maximum difference from
mean of observations (mm).....
Minimum number of readings/
observation..............................
Maximum difference from
mean of readings (mm)...........
3
10"
Observations per night ................ 16
16
2
Number of nights ....................... 2
Standard deviation of mean
not to exceed .......................... 0.45" 0.45"
Rejection limit from the mean .... 5"
5"
§
§
§
§
1
2
. 10''.
2
io"
1
1:j:
10
10:j:
10
10
10
10
§
§
§
§
2••
1 ••
1 ••
1 ••
150
150
200
200
20
20
10
JO
§
§
§
§
(.
Measurements of astronomic •latitude and longitude
are not required in the United States, except perhaps for
first-order work, because sufficient information for deter­
mining deflections of the vertical exists. Detailed proce­
dures can be found in Hoskinson and Duerksen (1952).
2
2.0"
5"
2
Order
Class
20"
12
1
8
1
4
1
0.6"
5"
1.0"
6"
1.7"
6"
c·
1
t
First
Second
I
Second
II
Third
I
Third
II
Azimuth closure
at azimuth
checkpoint
(seconds of arc) . 1.7yN 3.0yN 4.SyN 10.0yN 120yN
, Position closure.... 0.04 yK 0.08yK 0.20yK 0.40yK 0.80yK
after azimuth ...
or
or
or
or
or
adjustmentt ..... 1:100,000 1:50,000 1:20,000 1:10,000 1:5,000
(N is number of segments, K is route distance in km)
The expression containing the square root is designed for longer lines where
higher proportional accuracy is required. Use the formula that gives the smallest
permissible closure. The closure (e.g., 1:100,000) is obtained by computing the
difference bet.ween the computed and fJXCd values, and dividing this difference by K
Note: Do not confuse closure with distance accuracy of the survey.
t
Electro-Optical Distances
r �-/
10
Office Procedures
Astronomic Azimuths
Minimum number of
measurements .........................
Minimum number of concentric
observations/measurement......
Minimum number of offset
r�'-1 observations/measurement......
Maxi�umdifference from
0
mean of observations (mm)..... 60
10
8 if 0.2", 12 if 1.0" resolution.
• 6 if 0.2", 8 if 1.0" resolution.
§ as specified by manufacturer.
; only if decimal reading near O or high 9'.s.
•• carried out at both ends of the line.
Reciprocal Vertical Angles
(along distance sight path)
Number of independent
observations direct/reverse ..... 3
Maximum spread........................ 10"
Maximum time interval between
reciprocal angles (hr) ..............
10
Microwave Distances
First Second Second T�itd · Third
I
II
I
II
Directions
10
Infrared Distances
'---./�
Number of positions.................... 16 8 or 12t 6 ors•
4
Standard deviation of mean
not to exceed .......................... 0.4" 0.5''
0.8"
1.2"
5"
5"
Rejection limit from the mean.... 4"
5"
Minimum number of readings/
observation (or equivalent) ..... 10
Maximum difference from
mean of readings (mm)........... §
Minimum number of
measurements ......................... 1
Minimum number of concentric
observations/measurement......
Minimum number of offset
observations/measurement......
Maximum difference from
mean of observations (mm)..... 10
Minimum number of readings/
observation.............................. 10
Maximum differen:ce from
mean of readings (mm} ........... §
Field Procedures
Theodolite observations for first-order and second-order,
class I surveys may be made only. at night. Electronic
distance measurements need a record at both ends . of the
line of wet and dry bulb temperatures to :l;: 1 • C and
barometric pressure to ±5 mm of mercury. The theodo­
lite, EDM, and targets should be centered to within 1 mm
over the survey mark or eccentric point.
Order
Class
First Second Second Third Third
I
II
I
II
Order
Class
First Second Second Third Third
I
II
I
II
·1
A minimally constrained least squares· adjustment will
be checked for blunder_s by examining the nonpalized
residuals. The observation weights will be checked by
60
3-4
receive an accuracy classification, it must be permanently
monumented.
A grid of intersecting lines should . contain a minimum
of eight network points, and should have a network con­
trol point at each corner. The remaining network control
points may be distributed about the interior or the periphery
of the grid. However, there should be at least one network
control point at an intersection of the grid lines near the
center of the grid. If the required network points are not
available, then they should be established by some other
measurement system. Again, the horizontal datum values
of these network control points must have an order (and
class) better than the intended order (and class) of the
new survey.
inspecting the postadjustment estimate of the variance of
unit weight Distance standard errors computed by error
propagation in a correctly weighted least squares adjust­
ment will indicate the provisional accuracy classification.
A survey variance factor ratio will be computed to check
for systematic error. The least squares adjustment will
use models which account for the following:
(a = 6378137 m)
semimajor axis of the ellipsoid
reciprocal flattening of the el!ipsoid
mark elevation above mean sea level
geoid heights
deflections of the vertical
geodesic correction
skew normal correction
height of instrument
height of target
sea level correction
arc correction
geoid height correction
second velocity correction
crustal motion
(1/f = 298.257222)
· (known to 1 m)
(known to ±6 m)
(known to ±3")
±
3.4 Inertial Surveying
Inertial surveying is a measurement system comprised
of lines, or a grid, of Inertial Surveying System (ISS)
observations. These specifications cover use of .inertial .
systems only for horizontal control
(,/'. J
Network Geometry
Order
Class
Second Second - Third
Third
I
II
I
Station spacing not less than (km) .... 10
Maximum deviation from straight
line connecting endpoints .............. 20°
4
2
1
°
°
35 °
25
30
II
Each inertial survey line is required to tie into a mini­
mum of four horizontal network control points spaced.
well apart and should begin and end at network control
points. These network control points must have horizontal
datum values better than the intended order (and class) of
the new survey. Whenever the shortest distance between
two new unconnected survey points is Jess than 20 percent
of the distance between those points traced along existing
or new connections, then a direct connection should be
made between those two survey . points. In addition, the
survey should connect to any· sufficiently accurate net­
work control points within the distance specified by the
station spacing. The connections may be measured by
EDM or tape traverse, or by another ISS line. If an ISS
line is used, then these lines should follow the same specifications as all other ISS lines in the survey.
For extended area surveys by ISS, a grid of intersecting
lines that satisfies the 20 percent rule stated above can be
designed. There must be a mark at each intersection of the
lines. This mark need not be · l:l permanent monument; it
may be a stake driven into the ground. For a position to
Instrumentation
ISS equipment falls into two types: analytic (or strapdown)
and semianalytic. Analytic inertial units are not consid­
ered to possess geodetic accuracy. Semianalytic units are
either "space stable" or "local level." Space stable sys­
tems maintain the orientation of the platform with respect
to inertial space. Local level systems continuously torque
the accelerometers to account for Earth rotation and
movement of the .inertial unit, and also torque the platform to
coincide with the local level. This may be done on com­
mand at a coordinate update, or whenever the unit achieves
zero velocity (Zero velocity UPdaTe, or "ZUPT"). Inde­
pendently of the measurement technique, the recorded
data mayc be filtered by an onboard computer. Because
of the variable quality of individual ISS instruments,
the user should test an instrument with existing geodetic
control beforehand.
An offset measurement device accurate to within. 5 mm
should be affixed to the inertial unit or the vehicle.
Calibration Procedures
A static calibration should be performed yearly and
immediately after repairs affecting the platform, gyro­
scopes, or accelerometers.
A dynamic or field calibration should be performed
prior to each project or subsequent to a static calibration.
The dynamic calibration should be performed only between
horizontal control points of first-order accuracy and in
each cardinal direction. The accelerometer scale factors
from this calibration should be recorded and, if possible,
stored in the onboard computer of the inertial unit.
Before each project or after repairs affecting the offset
measurement device or the inertial unit, the relation between
the center of the inertial unit and the zero point of the
offset measurement device should be established.
Field Procedures
When sur,veying in a helicopter, the helicopter must
come to rest on the ground for all ZUPT's and all
measurements.
3-5
(-\._
✓
'--- �j')
Order
Class
Second Second
I
11
Minimum number of complete
runs per line .................................
2
Maximum deviation from a
uniform rate of travel
(including ZUPT) ........................ 15%
Maximum ZUPT interval (ZUPT
to ZUPT) (sec) ............................ 200
Third
I
11
20%
25%
30%
240
300
300
Office Procedures
Second Second
Maximum difference of smoothed-...
coordinates between forward
and reverse run ( cm) ....................
I
11
60
60
Third
Third
70
80
I
11
A minimally constrained least squares adjustment of
the raw or filtered survey data will be checked for blunders
by examining the normalized residuals. The observation
weights will be checked by inspecting the postadjustment
estimate of the variance of unit weight. Distance standard
errors computed by error propagation in this correctly
weighted least squares adjustment will indicate the provi­
sional accuracy classification. A survey variance factor
ratio will be computed to check for systematic error. The
least squares adjustment will use the best availa61e model
for the particular inertial system. Weighted averages of
individually smoothed lines are not considered substitutes
for a combine<i least squares adjustment to achieve geodetic
accuracy.
Network Geometry
LJ�--'
First First Second Second Third
I
Bench mark spacing not
more than (km) ...................... 3
Average bench mark spacing
not more than (km) ................. 1.6
11
I
II
3
3
3
3
11
Line length between network
control points not more
than (km) ............................... 300
100
50
25
50
( double-run)
25
10
(single-run)
Distance, survey
to network
Maximum spacing of
extra connections (km)
0.5 km or less ...................................
0.5 km to 2.0 km ..............................
20 km to 3.0 km ..............................
10
20
1.6
1.6
�.o
3.0
5
First First Second Second
I
I
11
11
Third
Leveling instrument
Minimum repeatability of
line of sight .......................... 0.25" 0.25" 0.50"
Leveling rod construction......... IDS IDS IDSt
or ISS
0.50" 1.00"
ISS Wood or
Metal
Instrument and rod resolution
(combined)
Least count (mm) ..................... 0.1
1.0
0.1 0.5-1.0*
(IDS-Invar, double scale)
(ISS-Invar, single scale)
t if optional micrometer is used.
• 1.0 mm ·if 3-wire method, 0.5 mm if optical micrometer.
3-6
I __
I
Order
Class
Geodetic leveling is a measurement system comprised
of elevation differences observed between nearby rods.
Leveling is used to extend vertical control.
_,. . r . ·)
11
ln$trumentation
3.5 Geodetic Leveling
Order
Class
I
New surveys are required to tie to existing network
bench marks at the beginning and end of the leveling line.
These network bench marks must have an order (and
class) equivalent to or better than the intended order (and
class) of the new survey. First-order surveys are required
to perform check connections to a minimum of six bench
marks, three at each end. All other surveys require a
minimum of four check connections, two at each end.
"Check connection" means that the observed elevation
difference agrees with the adjusted elevation difference
within the tolerance limit of the new survey. Checking the
elevation difference. between two bench marks located on
the same structure, or so close together that both may
have been affected by the same localized disturbance, is
not considered a proper check. In addition, the survey is
required to connect to any network control points within 3
km of its path. However, if the survey is run parallel to
existing control, then the following table specifies th�
maximum spacing of extra connections between the survey
and the control. At least one extra connection should
always be made.
A complete ISS measurement consists of measurement
of the line while traveling in one direction, followed by
measurement of the same line while traveling in the re­
verse direction (double-run). A coordinate update should
not be performed at the far point or at midpoints of a line,
even though those coordinates may be known.
The mark offset should be measured to the nearest 5
mm.
Order
Class
First First Second Second Third
Order
Class
Third
1.0
(
(
Field Procedures-Continued
Only a compensator or tilting leveling instrument with
an optical micrometer should be used for first-order leveling.
Leveling rods should be one piece. Wooden or metal rods
may be employed only for third-order work. A turning
point consisting of a steel turning pin with a driving cap
· should be utilized. If a steel pin cannot be driven, then a
turning plate ("turtle") weighing at least 7 kg should be
substituted. In situations allowing neither turning pins
nor turning plates (sandy or marshy soils), a long wooden
stake with a double-headed nail should be driven to a firm
depth.
Order
Class
Calibration Procedures
Order
Class
First First Second Second Third
I
I
II
II
Leveling instrument
Maximum collimation error,
single line of sight (mm/m) .... 0.05 0.05 0.05
Maximum collimation error,
reversible compensator type
instruments, mean of two
lines of sight (mm/m) ............. 0.02 0.02 . 0.02
Time interval between collimation
error determinations not
longer than (days)
.7
Reversible compensator ...... 7
7
1
Other types .........................
1
1
· Maximum angular difference
between two lines of sight,
40"
reversible compensator ........... 40" 40"
Leveling rod
Minimum scale calibration
standard.................................. N
Time interval between
scale calibrations (yr) ............. .
Leveling rod bubble verticality
maintained to within ............... 10'
0.05
0.02
0.10
0.04
7
1
7
7
40"
60"
N
N
M
M
10'
10'
10'
10'
Nonreversible compensator
leveling instruments
Off-level/relevel
instrument between
observing the high
and low rod scales...........
5
10
10
10
10
10
60
70
90
0.5
0.5
0.5
0.5
yes
yes
yes
yes
yes
4yD
6yD
8yD
12yD
5yE
6yE
8yE
12yE
yes
yes
yes
yes
yes
yes
2
2
3
yes
yes
yes
1.00
1.00
2.00
2.00
0.30
0.30
0.60
0.70
1.30
0.60
0.70
1.30
(SRDS-Singlo-Run, Double Simultaneous procedure)
(DR-Doublo-Run)
(SP-SPur, less than 2� km, doublo-run)
D-shortest length of section (ono-way) in km
£-perimeter <if loop in km
t Must doublo-run when using 3-wirc method.
• May single-run if line length between network control points is less than
25km.
§ May single-run if line length between network control points is less than
10km.
Field Procedures
First
Il
Single-run methods
Reverse direction of single
runs every half day.........
5
10
Second Second Third
I
II
60
Double scale rods
Low-high scale elevatiqn
difference for one setup
not to exceed (mm)
With reversible
compensator ........... 0.40
Other imtrument types:
Half-centimeter rods .... 0.25
Full-centimeter rods ... 0.30
Compensator-type instruments should be checked for
proper operation at least every 2 weeks of use. Rod
calibration should be repeated whenever the rod is dropped or
damaged in any way. Rod levels should· be checked for
proper alignment once a week. The manufacturer's
calibration standard should, as a minimum, describe scale
behavior with respect to temperature.
First
I
Difference of forward and
backward sight lengths
never to exceed
2
per setup (m) ..............
4
per section (m) ...........
Maximum sight length (m) .. 50
Minimum ground clearance
of line of sight (m) ..... ,.... 0.5
Even number of setups
when not using leveling
rods with detailed
calibration ...................... yes
Determine temperature
gradient for the vertical
range of the line of sight
at each setup .................. yes
Maximum section
misclosure·(mm) ............ 3 yD
Maximum loop
misclosure (mm) ............ 4yE
First
II
3-wire method
Reading check (difference
between top and bottom
intervals) for one setup
not to exceed (tenths of
rod units) ........................
Read rod 1 first in
alternate setup method...
(N-National standard)
(M--;-Manufacturer's stand ard)
Order
Class
First
I
Second Second Third
l
11
Minimal observation
method .......................... micro- micro­ micro- 3-wire center
meter meter meter or
wire
3-wire
Section running .................. SRDS SRDS SRDS SRDS SRDS
or DR or DR or DRt or DR* or DR§
or SP or SP or SP
Double-run leveling may alway� be used, but single­
run leveling done with the double simultaneous procedure
may be used only where it can be evaluated by loop
closures. Rods should be leap-frogged between setups
3-7
3.6 Photogrammetry
(alternate setup method). The date, beginning and ending
times, cloud coverage, air temperature (to· the nearest
degree), temperature scale, and average wind speed should
be recorded for
. each section plus any changes in the date'
.
mstrumentation, observer or time zone. The instrument
n�d not be off-leveled/releveled between observing the
high and low scales when using an instrument with a
reversible compensator. The low-high scale difference
tolerance for a reversible compensator
for the
· is used only
.
.
control of blunders.
With double scale. rods, the following observing sequence
should be used:
PhotograD;1metry is a measurement system comprised
of photographs taken by a precise metric camera and
measured by a comparator. Photogrammetry is used for
densification of horizontal control. The following specifi­
cations apply only to analytic methods.
Network Geometry
Order
Class
Third
II
66%
66%
60%
20%
60%
20%
. 8
3
3
6yD
SyD 12yD
6yE
SyE 12yE
Instrumentation
First . First Second Second Third
Ii
II
I
I
Section misclosures
(backward and forward)
c:J
Third
I
The photogrammetric survey should be areal:- single
strips of photography are not acceptable. The survey should
en�ompass, ideally, a minimum of eight horizontal con:
trol points and four vertical points spaced about the
perimeter of the survey. In addition, the horizontal con­
trol points should be spaced no farther apart than seven
air bases. The horizontal control points should have an
order (and class) .better than the intended order (and class)
of the survey. The vertical points need not meet geodetic
con�ol standards. If the required control points are not
available, then they must be established by some other
measurement system.
Office Procedures
Algebraic sum of all
corrected section misclosures
of� leveling line
not to exceed (mm) ................. 3yD 4yD
Section misclosure not to
exceed (mm) ........................... 3yE . 4yE
Loop misclosures
Algebraic sum of all
corrected misclosures
not to exceed(mm) ................. 4yF 5yF
Loop misclosure not
to exceed(mm) ....................... 4yF 5yF
Second Second
II
I
Forward overlap not less than ........... 66%
Side overlap not Jess than ................. 66%
Intersecting rays per point not
9
less than(design criteria) ..............
backsight, low-scale
backsight, stadia
foresight, low-scale
foresight, stadia
off-leveJ/relevel or reverse compensator
foresight, high-scale
backsight, high-scale
Order
Class
Order
Class
6yF
SyF 12yF
6yF
SyF 12yF
(_
(
Second Second
II
I
Third
I
Third
II
Metric Camera
Maximum warp of platen not
10
10
more than (µm) .................. ,......... 1�
10
Dimensional control not
Jess than........................................ reseau
8
8
8
with fiducials fiducials fiducials
maximum
spacing
of 2 cm
(O-hortest length of leveling line (on(}-way) in km)
(8-hortest on(}-way length of section in km)
(F-length of loop in km)
The normalized residuals from a minimally constrained
least squares adjustment will be checked for blunders.
The observation weights will be checked by inspecting the
postadjustment estimate of the variance of unit weight.
Elevation difference standard errors computed by error
P1:°P8:ga�on in a correctly weighted least squares adjustment
will mdicate the provisional accuracy classification. A
survey variance factor ratio will be computed to check for
systematic error. The least ;quares adjustment will use
models that account for:
Comparator
Least count(µm) ..............................
The camera should be of at least the quality of those
employed for large-scale mapping. A platen should be
included onto which the film must be satisfactorily flat­
tened during exposure. Note that a reseau should be used
for second-order, class I surveys.
Calibration Procedures
gravity effect or orthometric correction
rod scale errors
rod(Invar) temperature
refraction-need latitude and longitude to 6" or vertical tempera­
ture difference. observations between 0.5 and 2.5 m above the
ground
earth tides and magnetic field
collimation error
crustal motion
Order
Class
Metric camera
Root mean square of calibrated
radial distortion not more
than(µm) .....................................-
3-8
Second Second
I
II
3
Third
I
Third
II
3
5
-�
()
(L
A least squares adjustment of the photocoordinates,
constrained by the coordinates of the horizontal and ver­
tical control points, will be checked for blunders by examin­
ing the normalized residuals. The observation weights
will be checked by inspecting the postadjustment esti­
mate of the variance of unit weight. Distance standard
errors computed by error propagation in this correctly
weighted least squares adjustment will indicate the provi­
sional accuracy classification. A survey variance factor
ratio will be computed to check for systematic error. The
least squares adjustment will use models that incorporate
the quantities determined by calibration.
Calibration Procedures-Continued
Order
Class
Second Second
11
I
Third
I
Third
II
st
st
st
3
3
3
3
Root mean square of calibrated
decentering distortion not more
than (!Lm) .....................................
Root mean square of reseau
coordinates not more than (!Lm) ....
Root mean square of fiducial
coordinates not more than (!Lm) ....
t not usually treated separately in camera calibration facilities; manufacturer's
certification is satisfactory.
The metric camera should be calibrated every 2 years,
and the comparator should be calibrated every 6 months.
These instruments should also be calibrated after repair
or modifications.
Characteristics of the camera's internal geometry (radial
symmetric distortion, decen�ered lens distortion, princi­
pal point and point of symmetry coordinates, arid reseau
coordinates) should be determined using recognized cali­
bration techniques, like those described in the. current
edition of the Manual of Photogrammetry. These charac­
teristics will be applied as corrections to the measured
· image coordinates.
3.7 Satellite Doppler Positioning
Satellite Doppler positioning is a three-dimensional
measurement system based on the radio signals of the
U.S. Navy Navigational Satellite System (NNSS),
commonly referred to as the TRANSIT system. Satellite
Doppler positioning is used primarily to establish hori­
zontal control.
The Doppler observations are processed to determine
station positions in Cartesian coordinates, which can be
transformed to geodetic coordinates (geodetic latitude
and longitude and height above reference ellipsoid). There
are two methods by which station positions can be derived:
point positioning and relative positioning.
Point positioning, for geodetic applications, requires
that the processing of the Doppler data be performed with
the precise ephemerides that are supplied by the Defense
Mapping Agency. In this method, data from a single
station is processed to yield the station coordinates.
Relative positioning is possible when two or more receivers
are operated together in the survey area. The processing
of the Doppler data can be performed in four modes:
simultaneous point positioning, translocation, semishort
arc, and short arc. The specifications for relative positioning
are valid only for data reduced by the semishort or short
arc methods. The semishort arc mode allows up to 5
degrees of freedom in the ephemerides; the short arc mode
allows 6 or more degrees of freedom. These modes allow
the use of the broadcast ephemerides in place of the
precise ephemerides.
The specifications quoted in the following sections are
based on the experience gained from the analysis of Doppler
surveys performed by agencies of the Federal gov�rn­
ment. Since the data are primarily from surveys performed
within the continental United States, the precisions and
related specifications may not be appropriate for other
areas of the world.
Field Procedures
Photogrammetry invoives hybrid measurements: a metric
camera photographs targets and features in the field, and
a comparator measures these photographs in an office
environment. Although this section is entitled "Field Pro­
cedures," it deals with the actual measurement proce�s
and thus includes comparator specifications.·
Order
Class
Targets
Control points targeted .....................
Pass points targeted ..........................
Comparator
Pointings per target not less than ......
Pointings per reseau (or fiducial)
not less than ..................................
Number of different reseau
intersections per target not
Jess than ........................................
Rejection limit from mean of
paintings per target (!Lm) ..............
Second Second Third
I
11
I
Third
II
yes
yes
yes
yes
4
3
2
2
4
3
2
2
3
3
3
Second Second Third
I
II
I
Third
11
6
12
yes
yes
optional optional
4
3
Office Procedures
f-~C)
�-,/
Order
Class
Root me1rn square of adjusted
photocoordinates not more
than (!Lm) .....................................
4
8
Network Geometry
The order of a Doppler survey is determined by: the
spacing between primary Doppler stations, the order of
the base network stations from which the primaries are
established, and the method of data reduction that is
used. The order and class of a survey cannot exceed the
3-9
,.;
lowest order (and class) of the base stations used to estab­
lish the survey.
The primary stations should be spaced at regular inter­
vals which meet or exceed the spacing required for the
desired accuracy of the survey. The primary stations will
carry the same order as the survey.
Supplemental stations may be established in the same
survey as the primary stations. The lowest order (and
class) of a supplemental station is determined either by its
spacing with, or by the order of, the neares� Doppler or
other horizontal control station. The processing mode
determines the allowable station spacing.
In carrying out a Doppler survey, one should occupy,
using the same Doppler equipment and procedures, at
least two existing horizontal network (base) stations of
order (and class) equivalent to, or better than, the intended
order (and class) of the Doppler survey. If the Doppler
survey is to be first-order, at least three base stations
must be occupied. If relative positioning is to be used, all
base station base lines must be directly observed during
the survey. Base stations should be selected near the
perimeter of the survey, so as to encompass the entire
survey.
Stations which have a precise elevation referenced by
geodetic leveling to the National Geodetic Vertical Datum
(NGVD) are preferred. This will allow geoidal heights to
be determined. As mariy base stations as p<:>ssible should
be tied to the NGVD. If a selection is to be made, those
stations should be chosen which span· the largest portion
of the survey.
If none of the selected base stations is tied to the
NGVD, at least two, preferably more, bench marks of the
NGVD should be occupied. An attempt should be made
to span the entire survey area.
Datum shifts for transformation of point position solu­
tions should be derived from the observations made on the
base stations.
The minimum spacing, D, of the Doppler stations may
be computed by a formula determined by the processing
mode to be employed. This spacing is also used in con­
junction with established control, and other Doppler
control, to determine the order and class cif the supple­
mental stations.
By using the appropriate formula, tables .can be con­
structed showing station spacing as a function of point or
relative one-sigma position precision (sp or sr) and desired
survey (or station) order.
Order
Class
First Second Second Third Third
II
1
11
1
sp (cm)
200 ............................................. 566
100 ............................................. 283
70 ............................................... 200
50 ............................................... 141
242
141
100
71
D(km)
114
57
40
26
56
28
20
14
28
14
10
(
7
Relative Positioning
D = 2 sr3where
a = denominator of distance accuracy classification
standard (e.g., a= 100,000 for first-order standard).
Order
Class
First Second Second Third Third
II
11
I
I
sr (cm)
D(km)
20
14
8
50 ............................................... 100
35 ............................................... 70
20 ..............................,,............... 40
50
35
20
10
7
4
5
4
2
However, the spacing for relative positioning should
not exceed 500 km.
Instrumentation
The receivers should receive the two carrier frequen­
cies transmitted by the NNSS. The receivers should record
the Doppler count of the satellite, the receiver clock
times, and the signal strength. The integration interval
should be approximately 4.6 sec. Typically six or seven of
these intervals are accumulated to form a 30-second
Doppler count observation. The reference frequency should
be stable to within 5.0(10-11) per 100 sec. The maximum
difference from the average receiver delay should not
exceed 50 µsec. The best estimate of the mean electrical
center of the antenna should be marked. This mark will be
the reference point for all height-of-antenna measurements.
(
Calibration Procedures
Receivers should be calibrated at least once a year, or
whenever a modification to the equipment is made. It is
desirable to perform a calibration before every vroject to
verify that the equipment is operational. The two-receiver
method explained next is preferred and should be used
whenever possible.
Two-Receiver Method
The observations are made on a vector base line, of
internal accuracy sufficient to serve as a comparison
standard, 10 to 50 m in length. The base line should be
located in an area free of radio interference in the 150 and
400 MHz frequencies. The procedures found in the tal;,le
on relative positioning in "Field Procedures" under the 20
cm column heading will be used. The data are reduced by
either shortarc or semishort arc methods. The receivers
Point Positioning
where
a == denominator of distance accuracy classification
standard (e.g., a = 100,000 for first-order stand­
ard).
3-10
\...
will be considered operational if the differences between
the Doppler and the terrestrial base line components do
not exceed 40 cm (along any coordinate axis).
Single-Receiver Method
Observations are made on a first-order station using
the procedures found in the table on relative positioning
in "Field Procedures" under the 50 cm column heading.
The dat� are reduced with the precise ephemerides. The
resultant position must agree within 1 m of the network
position.
Field Procedures
The following tables of field proceµures are valid only
for measurements made with the Navy Navigational Sa­
tellite System (TRANSIT).
Point Positioning
s (precise ephemerides)
P
50 cm
Max. standard deviation of mean
of counts/pass (cm), bfoadcast
ephemerides.................................. 25
Period of observation not less
than (hr) . ... .......... .... ... ... ...... ......... 48
Number of observed passes not
less thant ...................................... ·" 40
Number of acceptable passes
(evaluated by on-site point
processing) not less than................ 30
Minimum number of acceptable
6
passes within each quadrant*........
Frequency standard warm-up
time (hr)
crystal........................................... 48
atomic................................ :.......... 1.5
Maximum interval between
meteorological observations (hr)....
6
70 cm
JOO cm 200 cm
25
25
25
36
24
12
30
15
8
20
9
4
4
2
48
1.5
24
1.0
24
1.0
§
§
§
t Number of passes refers to those for which the precise ephemerides are
available for reduction.
• There should be a nearly equal number of northward and southward passes.
§ each setup, visit and takedown.
Relative positioning
s,
Maximum standard deviation of mean of
counts/pass (cm), broadcast ephemerides ...
Period of observation not less than (hr) ...........
Number of observed passes not less thant.......
Number of acceptable passes (evaluated
by on-site point position processing)
not less than ................................................
Minimum number of acceptable passes
within each quadrant* ................................
Frequency standard warm-up time (hr)
crystal.........................................................
atomic.........................................................
Maximum interval between meteorological
observations (hr) _.........................................
20 cm
35 cm
50 cm
25
48
40
25
36
30
25
24
15
30
20
9
6
4
2·
48
1.5
48
1.5
48
1.5
6
6
§
t Number of observed passes refers to all satellites available for tracking and
reduction with the broadcast or precise ephemerides.
• Number of northward and southward passes should be nearly equal.
§ Each setup, visit and takedown.
3-11
The antenna should be located where radio interference
is minimal for the 150 and 400 MHz frequencies. Medium
frequency radar, high voltage power lines, transformers,
excessive noise from automotive ignition systems, and
high power radio and television transmission antennas
should be avoided. The horizon should not be obstructed
above 7.5 ° .
The antenna should not be located near metal struc­
tures, or, when on the roof of a building, less than 2 m
from the edge. The antenna must be stably located within
1 mm over the station mark for the duration of the
observations. The height difference between the mark
and the reference point for the antenna phase center
should be measured to the nearest millimeter. If an antenna is
moved while a pass is in progress,· that pass is not accept­
able. If moved, the antenna should be relocated within 5
mm of the original antenna height; otherwise the data
may have to be processed as if two separate stations were
established. In the case of a reoccupation of an existing
Doppler station, the antenna should be relocated within 5
mm of the original observing height.
Long-term reference frequency drift should be moni­
tored to ensure it does not exceed the manufacturer's
specifications.
Observations- of temperature and relative humidity should
be collected, if possible, at or near the height of the phase
center of the antenna. Observations of wet-bulb and dry­
bulb temperature readings should be recorded to the nearest
0.5 • C. Barometric readings at the station site should be
recorded to the nearest millibar and corrected for differ­
ence in height between the antenna and barometer.
Office Procedures
The processing constants and criteria for determining
the quality of point and relative positioning results are as
follows:
1. For all passes for a given station occupation, the
average number of Doppler counts per pass should
be at least 20 (before processing).
2. The cutoff angle for both data points and passes
should be 7 .5 • .
3. For a given pass, the maximum allowable rejection
of counts, 3 sigma postprocessing, will be 10.
4. Counts rejected (excluding cutoff angle) for a solu­
tion should be less thap. 10 percent.
5. Depending on number of passes and quality of data,
the standard deviation of the range residuals for all
passes of a solution should range between:
Point positioning-IO to 20 cm
Relative positioning-5 to 20 cm
A minimally constrained least squares adjustment will
be checked for blunders by examining the normalized
residuals. The observation weights will be checked by
inspecting the postadjustment estimate of the variance of
unit weight. Distance standard errors computed by error
propagation between points in this correctly weighted
least squares adjustment will indicate the maximum . achiev-
gy considered sufficiently accurate for absolute gravity
measurements. An absolute instrument measures gravity
at a specific elevation above the surface, usually about 1
m. For this reason, the gravity value is referenced to that
level. A measurement of the vertical gravity gradient,
using a relative gravity meter and a tripod, must be made
to transfer the gravity value to ground level. The accuracy
of the relative gravimeter must satisfy the gravity gradi­
ent specifications found in "Field Procedures."
able accuracy classification. The formula presented in
"Standards" will be used to arrive at the actual classification.
The least squares adjustment will use models which ·account
. (--1
"/C1ror:
tropospheric scale bias, 10 percent uncertainty
receiver time delay
satellite/receiver frequency offset
precise ephemeris
tropospheric refraction
ionospheric refraction
long-term ephemeris variations
crustal motion
Calibration Procedures
Ballistic-laser instruments are extremely delicate and
each one represents a unique entity with its own charac­
teristics. It is impossible to identify common systematic
errors for all instruments. Therefore, the manufacturer's
recommendations for individual instrument calibration
should be followed rigorously.
· To identify any possible bias associated with a particular
instrument, comparisons with other absolute devices are
strongly recommended whenever possible. Comparisons
with previously established first-order, class I network
points, as well as first-order, class II network points tied
to the class I points, are also useful.
3.8 Absolute Gravimetry
Absolute gravimetry is a measurement system which
determines the magnitude of gravity at a station at a
specific time. Absolute gravity measurements are used to
establish and extend gravity control. Within the context
of a geodetic gravity network, as discussed in "Standards," a
series of absolute measurements at a control point is in
itself sufficient to establish an absolute gravity value for
that location.
The value of gravity at a point is time dependent, being
subject to dynamic effects in the Earth. The extent of
gravimetric stability can be determined only by repeated
observations over many years.
Field Procedures
__. .
The following specifications were determined from results
of a prototype device built by J. Faller and M. Zumberge
(Zumberge, M, "A Portable Apparatus for Absolute Mea­
surements of the Earth's Gravity," Department of Physics,
University of Colorado, 1981) and are given merely as a
guideline. It is possible that some of these. values may be
inappropriate for other instruments or models. Therefore,
exceptions to these specifications are allowed on a case­
by-case basis upon the recommendation of the manufac­
turer. Deviations from the specifications should be poted
upon submission of data for classification.
Q Network geometry cannot by systematized since abso­
;'
C
Network Geometry
lute observations at a specific location ar� discrete and
. uncorrelated with other points. In absolute gravimetry, a
network may consist of a single point.
A first-order, class l station must possess gravimetric
stability, which only repeated measurements can deter­
mine. This gravimetric stability should not be confused
with the accuracy determined at a specific time. It is
possible for a value to be determined very precisely at two
different dates and for the values at each of these respec­
tive dates to differ. Although the ultimate stability of a
point cannot be determined by a single observation ses­
sion, an attempt should be made to select sites which are
believed to be tectonically stable, and sufficiently distant
·from large bodies of water to minimize ocean tide coastal
loading.
The classification of first-order, class I is reserved for
network points which have demonstrated long-term sta­
bility. To ensure this stability, the point shou1d be reobserved
at least twice during the year of establishment and there­
after at sufficient intervals to ensure the continuing sta­
bility of the point. The long-term drift should indicate
that the value will not change by more than 20 µGal for at
least 5 years. A point intended as first-order, class I will
initially be classified as first-order, class II until stability
during the first year is demonstrated.
Order
Class
(_)�/
First
I
First
II
Second Third
20
20
50
100
5
s
5
5
12
12
37
48
4
4
5
5
5
5
5
10
Absolute measurement
Standard deviation of each
accepted measurement set
not to exceed (µGal) .....................
Minimum number of sets/
observation....................................
Maximum difference of a
measurement set from mean of
all measurements (µGal) ..............
Baroinetric pressure standard
error (mbar) .................................
Gradient measurement
Standard deviation of measurement
of vertical gravity gradient at
time of observation (µGal/m) .......
Standard deviation of height of
instrument above point (mm) ........
_J , Instrumentation
!
c·
The system currently being used is a ballistic-laser
device and is the only one at the current state of technolo3-12
(
Office Procedures
The manufacturer of an absolute gravity instrument
usually provides- a reduction process . which identifies and
accounts for error sources and identifiable parameters.
This procedure may be sufficient, making further office
adjustments unnecessary.
A least squares adjustment will be checked for blun­
ders by examining the normalized residuals. The observation
weights will be checked by inspecting the postadjustment
estimate of the variance of unit weight. Gravity value
standard deviations compu�ed by error propagation in a
correctly weighted, least squares adjustment will indicate
the provisional accuracy classification. The least squares
adjustment, as well as digital filtering techniques and/or
sampling, should use models which account for:
atmospheric mass attraction
microseismic activity
instrumental characteristics
lunisolar attraction
elastic and plastic response of the Earth (tidal loading)
3.9 Relative _Gravimetry
Relative gravimetry is a measurement system which
determines the difference in magnitude of gravity between
two stations. Relative gravity measur�ments · are used to
extend and densify gravity control.
Network Geometry
A first-order, class I station must possess gravimetric
stability, which only repeated measurements can deter­
mine. This gravimetric stability should not be confused
with the accuracy determined at a specific time. It is
possible for a value to be determined very precisely at two
· different dates, and for the values at each of these respec­
tive dates to differ. Although the ultimate stability of a
point cannot be determined by a single observation ses­
sion, an attempt should be made to select sites which are
believed to be tectonically stable.
The classification of first-order, class I is reserved for
network points that have demonstrated long-term sta­
bility. To ensure this stability, the point should be reobserved
at least twice during the year of establishment and there­
after at sufficient intervals. The long-term drift should ·
indicate that the value will not change by· more ·than the
20 µGal for at least 5 years. A point intended as first-order,
class I will initially be classified as first-order, class II
until stability during the first year is demonstrated.
The new survey is required to tie at least two network
poip.ts, which should have an order (and class) equivalent
to or better than the intended order (and class) of the new
survey. This is required to check the validity of existing
network points as well as to ensure instrument calibration.
Users are encouraged to exceed this minimal require­
ment. However, if one of the network stations is a first­
order, class I mark, then that station alone can satisfy the
minimum connecting requirement if the intended order of
the new survey is less than first-order.
Instrumentation
Regardless of the type of a relative gravimeter, the
internal error is of primary concern.
Order
Class
Minimum instrument internal
error (one-sigma), (µGal) ..............
First
First
10
10
I
II
Second Third
20
30
The instrument's internal accuracy may be determined
by performing a r�lative survey over a calibration line (see
below) and examining the standard deviation of a single
· reading. This determination should be performed after
the instrument is calibrated using the latest calibration
information. Thus the internal error is the measure of
instrument' uncertainty after all possible systematic error
sources have been eliminated by calibration.
Calibration Procedures
An instrument should be properly calibrated before a
geodetic survey is performed. The most important cali­
bration item is the determination of the mathematical
model that relates dial units, voltage, or some other
observable to milligals. This may consist only of a scale
factor. In other cases the model may demonstrate nonlin­
. earity or periodicity. Most manufacturers provide tables
or scale factors with each instrument. Care must be taken
to ensure the validity of these data over time.
When performing first-order work, this calibration model
should be determined by a combination of bench tests and
field measurements. The bench tests are specified by the
manufacturer. A field calibration should be performed
over existing control points of first-order, class I or II.
The entire usable gravimeter range interval should be
sampled to ensure an uncertainty of less than 5 µGal. FGCC
member agencies have established calibration lines for
this specific purpose.
The response of an instrument to air pressure and tem­
perature should be determined. The meter should be adjusted
(?r calibrated for various pressures and temperatures so
that the allowable uncertainty from these sources does not
exceed the values in the table below.
The manufacturer's recommendations should be fol­
lowed to ensure that all internal criteria, such as galva­
nometer sensitivity, long and cross level or tilt sensitivity,
and reading line, are within the manufacturer's allowable
tolerances.
The response of an instrument due to local orientation
should also be determined. Systematic differences may be
due to an instrument's sensitivity to local magnetic varia­
tions. Manufacturers attempt to limit or negate such a
response. However, if a meter displays a variation with
· · (l
(�;
The modified ladder sequence also begins and ends at
the same network, point. However, not all the survey points
are observed twice during the sequence. Again, more than
one network point may be observed in the sequence.
The line sequence begins at a network point and ends at
a different network point A survey point in a line sequence is
usually observed only once.
One should always monitor the internal temperature of
the instrument to ensure it does not fluctuate beyond the
manufacturer's recommended limits. The time of each
reading should be recorded to the nearest minute.
respect to orientation, then one must either have the
instrument repaired by the manufacturer, or minimize
the effect by fixing the orientation of the instrument
throughout a survey.
First
I
Order
Class
Necessary for user to determine
calibration model .......................... Yes
Allowable uncertainty of
s
calibration model (µGal) ..............
Allowable uncertainty due to
external air temperature
changes (µGal) ..............................
Maximum uncertainty due to
external air pressure
changes (µGal) ..............................
Allowable uncertainty due to
other factors (µGal) ......................
3
First
II
Second
Third
Yes
Yes
No
s
10
15
Office Procedures
3
3
. ,
..
Order
2
...
Rejection limits
Maximum standard error of a
gravity value (µGal) ......................
Total allowable instrument
uncertainty (µGal) ........................
5
•
Field Procedures
'A relative gravity survey is performed. using a sequence
of measurements known as a loop sequence. There are
three common types: ladder, modified ladder, and line.
The ladder sequence begins and ends at the same net­
work point, with the survey points being observed twice
during the sequence: once in forward running and �mce in
backward running. Of course, more than one network
�-- /'\ point may be present in a ladder sequence. . .
.
L�--)
Order
Class
Model Uncertainties
Uncertainty of atmospheric mass
model (µGal) ................................
Uncertainty of lunisolar
attraction (µGal).......:....................
Uncertainty of Earth elastic and
plastic response to tidal
loading (µGal) ...............................
.
First
I
Minimum number of instruments
used in survey ............................... 2
Recommended number of
instruments used in survey ............ 3
Allowable loop sequence ................... a
Minimum number of readings at
each observation/instrument ......... s
Standard deviation of consecutive
readings (undamped) from
mean* not to exceed (µGal) ......... 2
Monitor external temperature and
air pressure ................................... • Yes
Standard deviation of temperature
measurements (" C) ...................... 0.1
Standard deviation of air pressure
measurement (mbar) ....................
Standard deviation of height of
instrument above point (mm) ........
First
II
2
3
a
a,b
s
2
V
1
a,b,c
/
2t
2
s
Yes
No
instrument calibrations
1) conversion factors
2) thermal response
3) atmospheric pressure response
No
0.1
10
(a-ladder)
(b-modified ladder)
(c--line)
t Although two readings are required, only one reading need be recorded.
• corrected for lunisolar attraction.
(
Second
Third
20
20
so
100
10
10
20
30
0.5
0.5
s
s
2
2
s
(.
(linear and higher order)
(if necessary)
(if necessary)
instrument dnft
1) static
2) dynamic
1
s
First
II
A least squares adjustment, constrained by the network
configuration and precision of established gravity con­
trol, will be checked for blunders by examining the nor­
malized residuals. The observation weights will be checked
by inspecting the postadjustment estimate of the variance
of unit weight. Gravity standard errors computed by error
propagation in a correctly weighted least squares adjust­
ment will· indicate the provisional accuracy classification.
A survey variance factor ratio will be computed to check
for systrmatic error. The least squares adjustment will
use models which account for:
Second Third
2
First
I
. --r)
atmospheric mass attraction
(if necessary)
Earth tides
1) lunisolar attraction
2) Earth elastic and plastic response
(if necessary)
(_
,--'
'"-...,...,..:
3-14
--��---- ----
4. Information
Federal, State, and local governments, and private
organizations contribute survey data from their field
operations. These are incorporated into the NGS data
base. NOAA has entered into formal agreements with
several Federal and State Government agencies whereby
NGIB publishes, maintains, and distributes geodetic data
received from these organizations. Guidelines and for­
mats have been established to standardize the data for
processing and inclusion into the NGS data base. These
formats are available to organizations interested in
participating in the transfer of their files to NOAA (appendix
C).
Upon completion of the geodetic data base manage­
ment system, · inform!l,tion generated from the data base
will be automatically revised. A new data output format is
being designed for both horizontal and vertical published
control information. These formats, which were necessi­
tated by the requirements of the new adjustments of the
horizontal and vertical geodetic networks, will be more
comprehensive than the present versions.
New micropublishing techniques are being introduced
in the form of computer-generated microforms. Some
geodetic data are available on magnetic tape, microfilm,
and microfiche. These services will be expanded as the
automation system is fully implemented. Charges for digital
data are determined on the basis of the individual requests,
and reflect processing time, materials, and postage. The
booklets Publications of the National Geodetic Survey
and Products and Services of the National Geodetic Sur-.
vey are available from NGIB.
For additional information, write:
Chief, National Geodetic Information
Branch, N/CG17
National Oceanic and Atmospheric Administration
Rockville, MD 20852
To order by telephone:
data: ....................................................... 301-443-8631
publications: ............................................301-443-8316
computer programs or digital data: ......... 301-443-86 23
Geodetic control data and cartographic information
that pertain to the National Geodetic Control Networks
are widely distributed by a component of the National
Geodetic Survey, the National Geodetic Information Branch
(NGIB). Users of this information include Federal, State,
and local agencies, universities, private companies, and
individuals. Data are furnished in response to individual
orders, or by an automatic mailing service (the mecha­
nism whereby users who maintain active geodetic files
automatically receive newly published data for specified
areas) . Electronic retrieval of data can be carried out
directly from the NGS data base by a user.
Geodetic control data for the national networks are
primarily published as standard quadrangles of 30' in
latitude by 30' in longitude. However, in congested areas,
the standard .quadrangles are 15' in latitude by 15' in
longitude. In most areas of Alaska, because· of the sparse­
ness of control, quadrangle units are 1 • in latitude by 1 •
in longitude. Data are now available in these formats for
all horizontal control and approximately 65 percent of the
vertical control. The remaining 35 percent are presented
in the old formats; i.e., State leveling lines and description
booklets. Until the old format data have been converted to
the standard. quadrangle formats, the vertical control
data in the unconverted areas will be available only by
complete county coverage. Field data and recently adjusted
projects with data in manuscript form are available from
NGS upon special request. The National Geodetic Con­
trol Networks are cartographically depicted on approxi­
mately 850 different control diagrams. NGS provides
other related geodetic information: e.g., geoid heights,
deflections of the vertical, calibration base lines, gravity
values, astronomic positions, horizontal and vertical data
for crustal movement studies, satellite-derived. positions,
UTM coordinates, computer programs, geodetic calcula­
tor programs, and reference materials from the NGS data
bases.
The NGIB receives data from all NOAA geodetic field
operations and mark-recovery programs. In addition, other
4-1
5. References
(Special reference lists � foilow appendixes A and B)
lication 4, U.S. Coast and Geodetic Survey, Rock.ville,
Md., 14 pp. (revision of Special Publication 247, by
Gossett, F., 1959, pp. 84-94).
Defense Mapping Agency, 1975: Field Operations Man­
ual-Doppler Point Positioning. Defense Mapping Agen­
cy Tech. Manual TM-T-2-52220, Department of
Defense, 76 pp.
Dewhurst, w.; 1983: Input Formats and Specifications of
the National Geodetic Survey Data Base, vol III: Gravity
control data, Federal Geodetic Control Committee,
Rock.ville, Md., 163 pp.
Floyd, R., 1978: Geodetic bench ma{ks, NOAA Manual
NOS NGS 1, National Oceanic and Atmospheric
Administration, Rock.ville, Md., 50 pp.
Gos�ett, F., }950, rev. 1959: Manual of geodetic triangu­
lation, Special Publication 247, U.S. Coast and Geo­
detic Survey, Washington, D.C., 205 pp.
Hoskinson, A, and Duerksen, J., 1952: Manual of geodetic
as_tronomy: determination of longitude, latitude, and
azimuth, Special Publication 237, U.S. Coast and Geo­
detic Survey, Washington, D.C., 205 pp.
Mussetter, W., 1941, rev. 1959: Manual of reconnais­
sance for triangulation, Special Publication 225, U.S.
Coast and Geodetic Survey, Washington, D.C. 100 pp.
Pfeifer, L., 1980: Input Formats and Specifications of the
National Geodetic Survey Data Base, vol I: Horizontal
control data, Federal Geodetic Control Committee,
Rock.ville, Md., 205 pp.
Pfeifer, L., and Morrison, N., 1980: Input Formats and
Specifications of the National Geodetic Survey Data
Base, vol. II: Vertical control data, Federal Geodetic
Control Committee, Rock.ville, Md. 136 pp.
Schomaker, M., and Berry, R., 1981: Geodetic lev�ling,
NOAA Manual NOS NGS 3. National Oceanic and
Atmospheric Administration, Rock.ville, Md. 209 pp.
Slama, C. (editor), 1980: Manual of Photogrammetry
( 4th edition), American Soi;:iety of Photogrammetry,
Falls Church, Va., 1056 pp.
Basic Geodetic Information
Bomford, G., 1980: Geodesy (4th ed.). Clarendon Press,
Oxford, England, 855 pp.
Defense Mapping Agency, 1981: Glossary of Mapping,
Charting, and Geodetic Terms (4th edition), Defense
Mapping Agency Hydrographic/Topographic Center,
Washington, D.C., 203 pp.
Mitchell, H., 1948: Definitions of terms used in geodetic
and other surveys, Special Publication 242, U.S..Coast
and Geodetic Survey, Washington, D.C., 87 pp.
Torge, W., 1980: Geodesy. Walter de Gruyter & Co., New
Yorlc, N.Y., 254 pp.
Vanicek, P., and Krakiwsky, E., 1982: Geodesy: The Con­
cepts. North-Holland Publishing Co., New York, N.Y.,
691 pp.
CC)
Standards and Specifications
Director of National Mapping, 1981: Standard Specifi­
cations and Recommended Practices for Horizontal
and Vertical· Control Surveys (3rd edition), Director
of National Mapping, Canberra, Australia, 51 pp.
Federal Geodetic Control Committee, 1974: Classifica­
tion, Standards of Accuracy, and General Specifica­
tions of Geodetic Control Surveys, National Oceanic
and Atmospheric Administration, Rock.ville, Md., 12
pp.
Federal Geodetic Control Committee, -1975, rev. 1980:
Specifications to Support Classification, Standards
of Accuracy, and General Specifications of 'Geodetic
Control Surveys, National Oceanic and Atmospheric
Administration, Rock.ville, Md., 46 pp.
Surveys and Mapping Branch, 1978 : Specifications and
Recommendations for Control Surveys and Survey
Markers, Surveys and Mapping B ranch, Ottawa,
Canada.
Manuals on Field Procedures
Baker, L., 1968: Specifications for horizontal control marks,
ESSA Tech. Memo. Coast and "Geodetic Survey Pub-
5-1
APPENDIX A
Governmental Authority
A.1 Authority
for Geodetic Control and Related Surveys was appointed
April 4, 1969. The FGCC Circular No. 1, "�xchange of
Information," dated October 16, 1972, prescnbes report­
ing procedures for the committee (vice Exhibit C of Cir­
cular A-16) (Federal Geodetic Control Committee 1972).
The Federal Coordinator for Geodetic Control and Relat­
ed Surveys, Department of Commer�, is responsible for
coordinating, planning, and executing national geodetic
control surveys and related survey activities of Federal
agencies, financed in whole or in part by Federal funds.
The Executive Directive (Bureau of the Budget 1967: p.
2) states:
. (1) The geodetic control needs of Government agen­
cies and the public at large are met in the most
· expeditious and economical manner possible with
available resources; and
(2) all surveying activities financed in whole or in part
by Federal funds contribute to the National Net­
works of Geodetic Control when it is practicable
and economical to do so.
The Federal Geodetic Control Committee assists �nd
advises the Federal Coordinator for Geodetic Control and
Related Surveys.
The U.S. Department of Commerce's National Qceanic
and Atmospheric Administration (NOAA) is responsible
for establishing and maintaining the basic national hori­
zontal, vertical, and gravity geodetic control networks to
meet the needs of the Nation. Within NOAA this task is
assigned to the National Geodetic Survey, a Division of
the Office of Charting and Geodetic Services within the
National Ocean Service. This responsibility has evolved
from iegislation dating back to the Act of February 10,
1807 (2 Stat. 4131 which created the first scientific Fed­
eral agency, known as the "Survey of the Coast." Current
authority is contained in United States Code, Title 33,
USC 883a, as amended, and specifically defined by Execu­
tive Directive, Bureau of the Budget (now the Office of
Management and Budget) Circular No. A-16, Revised
(Bureau of the Budget 1967).
To coordinate national mapping, charting, and survey­
ing activities, the Board of Surveys and Maps of the
Federal Government was formed December 30, 1919, by
Executive Order No. 3206. "Specifications for Horizon­
tal and Vertical Control" were agreed upon by Federal
surveying and mapping agencies and approved by the
Board on May 9, 1933. When the Board was abolished
March 10, 1942, its functions were transferred to the
Bureau of the Budget, now the Office of Management and
Budget, by Executive Order No. 9094. The basic survey
specifications continued in effect. Bureau of the Budget
Circular No. ,A.-16, published January 16, 1953, and
revised May 6, 1967 (Bureau of the Budget 1967), pro­
vides for the coordination of Federal surveying and map­
ping activities. "Classification and Standards of Accura­
cy of Geodetic Control Surveys," published March 1,
1957, replaced the 193� specifications. Exhibit C to Cir­
cular A-16, dated October 10, 1958 (Bureau of the Bud­
get 1958), established procedures for the required coordi­
nation of Federal geodetic and control, surveys performed
in accordance with the Bureau of the Budget classifica­
tions and standards.
The Federal Ge'odetic Control Committee (FGCC) was
chartered December 11, 1968, and a Federal Coordinator
A.2 References
Bureau of the Budget, 1967: Coordination of surveying
and mapping activities. Circular No. A-16, Revised,
May 6, 3 pp. Executive Office of the President, Bureau
of the Budget (now Office of Management and Bud­
get), Washington, D.C. 20503.
Bureau of the Budget, 1958: Programing and coordina­
tion of geodetic control surveys. Transmittal Memo­
randum No. 2, 1 p., and Exhibit C of Circular No.
A-16, 4 pp. Executive Office of the President, Bureau
of the Budget (now Office of Management and Bud­
get), Washington, D.C. 20503.
Federal Geodetic Control Committee, 1972: Exchange of
Information. Circular No. 1, Federal Geodetic Control
Committee, October 16, 6 pp.
A-1
APPENDIXB
Variance Factor Estimation
B.1 Introduction
The classification accuracies for the National Geodetic
Control Networks measure how well a survey can provide
position, elevation, and gravity. (More specifically, a dis­
tance accuracy is used for horizontal networks, and an
elevation difference accuracy is used for vertical networks.)
The interpretation of what is meant by "how well" con­
tains two parts. A survey must be precise, i.e., fairly free
of random error; it must also be accurate, i.e., relatively
free of systematic error. This leads to a natural question of
how to test for random and systematic error.
Testing for random error is an extremely broad subject,
and is not examined here. It is assumed that the standard
deviation of distance, elevation difference, or gravity pro­
vides an adequate basis to describe the amount of random
error in a survey. Furth�r, it is assumed that the· selection
of the worst instance of the classification accuracy com. puted at all points (or between all pairs of points) provides
a satisfactory means of classifying a new survey. This
procedure may seem harsh, but it allows the user of
geodetic control to rely better upon a minimum· quality of
survey work. The nominal quality of a survey could be
much higher.
Consider the method of observation equations (see
Mikhail (1976) for a general discussion):
where ½ is the vector of actual observations and La is the
vector described above.
Associated with the observation vector ½ is a symmet­
ric variance-covariance matrix l": , which contains infor11,
mation on observation precision and correlation.
The observation equation may now be written in linear­
ized form
AX=L+V
where V is a vector of residual errors and X is a vector of
corrections to the parameter vector �- The least squares
estimate of X is
X = (N(l": YA)·1 A1(l":L/1L
11,
where the superscripts and ·1 denote transpose and inverse
(of a matrix) respectively.
1
The estimate provides a new set of values for the
parameters by
If the observation model F(Xa) is nonlinear (that is, A is
not constant for any set of Xa), then the entire process,
starting with the first equation, must be iterated until the
vector X reaches a stationary point.
Once convergence is achieved, La, computed from the
first equation, is the vector of adjusted observations. The
vector of observation residual errors, V, is
where
La is a vector of computed values for the observations of
dimension n,
Xa is a vector of coordinate and model parameters of
dimension u, and
F is a vector of functions that describes the observations
in terms of the parameters.
The design matrix, A, is defined as
Estimates of parameter precision and correlations are
given by the adjusted parameter variance-covariance
matrix, l":x computed by
a
l":x = (A1(l":L/1A)·l.
a
where A is a matrix of differential changes in the observation
model F with respect to the parameters, �. evaluated at a
particular set of parameter values, X0• A vector of
observation misclosures is
The precision of any other quantity that can be derived
from the parameters may also be computed. Suppose one
wishes to compute a vector of quantities, S,
B-1
B.2 Global Variance Factor Estimation (k = 1)
The global variance factor, f, is simply the a posteriori
variance of unit weight, tr/, when given an a priori vari­
ance of unit weight, rr-02. equal to 1.
It can be shown that
from the adjusted parameters, Xa. A geometry matrix, G,
is defined as
E(Vt(�L,)"1V) = n - u. .
where G is a matrix of differential changes in the func­
tions, S, with respect to the parameters, Xa, evaluated at a
particular set of parameter values, X0• By the principle of
linear error propagation,
(
(Mikhail 1976: p. 287)
For a single variance factor
so that
�s=G �xGt
a
=
I }:(yt(}:�)-1v) n - u
or
or for f to be unbiased (Hamilton 1964, p. 130)
where �s is the variance-covariance matrix of the com­
puted quantities.
f
This last equation is important since its terms are vari­
ances and covariances such as those for distance or height
difference. Use of this equation assumes that the model is
· not too nonlinear, that the parameter vector � has been
adequately estimated by the method of least squares, that ·
the design matrix A, the geometry matrix 0-, a,p.d the
variance-covariance matrix of the observations �L are
known. This last assumption is the focal point fo¥ the
remainder of this appendix.
We must somehow estimate the n (n + 1)/2 elements
of };L· Usually, we know �L subject to some global vari­
ance factor, f. We would then assume that
where
};L = the "true" variance-covariance matrix of the ob­
servations
};f = initial estimate of variance-covariance matrix of
the observations
Our assumption aqout the the structure of � · relative
to a single factor usually suffices. But this assumption can
be improved if we generalize the idea. Consider a partition 'of
the observations into k homogeneous groups. We now
estimate k different local variance factors
= E(Vt(}:�)-lV) = yt(}:v-1y
n-u
n-u
,.
.
ytpy
.
. .
, where p 1s
Th1s 1s 1"dentlca1 to the C1orm cr20 = -n
-.
u
defined as cr5(}:�)- 1
Since we are given that u/= 1, then P = (� )·1• Then f
= tr/, as we wished to prove.
The derivation assumes that there is no bias in the
residuals (Mikhail 1976), i.e.,
E(V) = 0.
However, outliers, as well as systematic errors, can
produce a biased global variance factor. We must be
satisfied that the observations contain no blunders, and
that our mathematical model is satisfactory in order to
use the global variance factor.
Particular types of systematic errors-global scale or
orientation errors-are not detectable in a survey adjust­
ment. They will not bias the residuals and will not influ­
ence the global variance factor. For example, to detect .a
global scale error, it must be transformed into a local
scale error by addition of more data or measurements that
can discriminate between global and local.
B.3 Local Variance Factor Esfunation (k = 2,3,...)
Let us separate our observations into k homogeneous
groups, and assume that we know the variance-covariance
matrices of all k groups, �- , subject to k local variance
1
factors, fi. Then
-r \ As will be discussed later, we may also detect systematic
C�-) error if one of the variance components is based on certi­
fied network observations.
B-2
(
o(�
( \.../)
work can be discovered by local variance factor esti­
mation. Of course a systematic error, such as a scale
factor influencing both the network and the survey, would
continue to remain hidden.
A variety of methods has been proposed that can be used
to estimate local variance factors. Among them are Min­
imum Norm Quadratic Unbiased Estimation (MINQUE)
(Rao 1971), Iterated Mlnimum Norm Quadratic Estimation
(IMINQE) (Rao 1972), Almost Unbiased Estimation
(AUE) (Horn et al. 1975), and Iterated Almost Unbiased
Estimation (IAUE) (Lucas 1984). Underlying these methods
is the assumption that there is no bias in any group of
residuals; that is
B.4 Iterated Almost Unbiased Estimation
(IAUE)
The IAUE method (Lucas 1984) can be used to esti­
mate covariance elements as well as the variance ele­
ments of i1. However, in testing for systematic error we
are concerned only with the survey and the network vari­
ance factors (k = 2).
A:s suggested by the title, the method is iterative. We
start with the initial values
This assumption can be turned to our advantage in the
detection of local systematic error.
Consider the . partition of observations into a network
group, subscript N, and a survey group, subscript s (k ===
2). Then
� and L�, with � set to 1
Let
For an adjustment of the network only, we may estimate
L� =f�L�
and for �n adjustment of the survey only, we may estimate
L� = f�L�
We now iterate from i = 0 to convergence
where �•s is the global variance factor of the survey
observations computed by a least squares adjustment free
of outliers and known systematic errors.
With perfect information and an unbiased model we
compute fN = f'N and fs = f's· On the·other band, if
our model is biased, this may not be the case. In other
words, we have a linkage between systematic error and
consistent estimation of local variance factors.
Now assume that our network observations are certi­
fied as having no systematic error, and that we have
perfe�� �owledge of their weights. Then f'N = 1 and�
= i �- In the absence of residual bias in the survey, we
should compute fN = 1 and fs = f's· In fact, we could
impose a constraint on the computation, fN = 1, to ensure
this result. A survey systematic error could. then manifest
itself as an increase in fs over f's·
There is no guarantee that systematic error in a survey
will increase fs over f's· For exan;iple, a survey may be
connected to the network at only one control point. A scale
error local to the survey would remain undetectable with
combined variance factor estimation. With a second con­
nection to the network, the survey scale error will begin to
be detectable. A:s the survey is more closely connected to
the network, the· capability to detect a survey scale error
becomes much better. We see that systematic error in a
survey that is well-connected to a certified geodetic net-
1) Perform least squares adjustment for
:X = (A'P[�)-1 A'PLL
2) L\is' = (Pk)- 1 - A8 (A'PLA)- 1 A�
1
3) fi+l _ (Vk) PkVk
s
- tr(��5Pk)
where tr is the trace function.
We test for convergence by
where E is a preset quantity > 0. The local survey variance
factor is
IT fk
In"
fs =
B-3
i=O
of the normal equations. Thus, the usual apparatus of
sparse least squares adjustments can be retained.
where m is the number of iterations to convergence. We
can then compute a survey variance factor ratio,
fs/f's
B.5 References
Computer simulations have shown that when the sur­
vey variance factor ratio exceeds 1.5, then the survey
contains systematic error. This rule becomes less reliable
when a survey is minimally connected to a network.
We note that for k = 1, the third step of the method
yields
Hamilton, Walter Clark, 1964: Statistics in Physical
Science, The Ronald Press Company, New York.
Horn, S.D., Horn, RA, and Duncan, D.B., 1975: Estimat­
ing heteroscedastic variances in linear models, Journal
of the American Statistical Association, 70, 380-385.
Lucas, James R., 1984: A variance component estimation
method for sparse matrix applications, unpublished
manuscript, NOS, NOAA, Rockville, Md.
Mikhail, Edward M., 1976: Observations and Least Squares,
IBP-A Dun-Donnelley publisher, New York.
Rao, C.R., 1972: Estimation of variance and covariance
components in linear models, Journal of the American
Statistical Association, 67, 112-115.
Rao, C.R.,· �9?1: Estimation of variance and covariance
components-MINQUE theory, Journal of Multivan"ate
Analysis, 1, 257-275.
(vipv)i
n-u
It is immediately recognized as the a posteriori esti­
mate of the variance of unit weight. In this special case,
IAUE convergence is correct, immediate, and unbiased.
The IAUE method is particularly attractive from a
computational point of view. If liL is diagonal, or nearly
so, then the requisite elements of liL may · be computed
from elements of lix thi�.t lie completely within the profile
(
(
B-4
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APPENDIXC
Procedures for Submitting Data to the National Geodetic Survey
cal Network. Gravity control surveys must be accom­
plished to at least second-order standards and tied to the
National Geodetic Gravity Network. Third-order gravi­
ty surveys ("detail" surveys) will be accepted by NGS for
inclusion into the NGS Gravity Working Files only in
accordance with the above mentioned FGCC publication.
A clear and accurate station description should be pro­
vided for all control points.
The original field records (or acceptable copies), .including
sketches, record books, and project reports, are required.
NGS will retain these records in the National Archives.
This is necessary if questions arise concerning the surveys
on which the adjusted data are based. In lieu of the
original notes, high quality photo copies and microfilm are
acceptable. The material in the original field books or
sheets are needed, not the abstracts or intermediate
computations.
Reconnaissance reports should be submitted before begin­
ning the field measurements, describing proposed con­
nections to the national network, the instrumentation,
and the field procedures to be used. This will enable NGS
to comment on the proposed survey, drawing on the informa­
tion available in the NGS data base concerning the accu­
racy and condition of these points, and to detennine if the
proposed survey can meet its anticipated accuracy. This
project review saves the submitting agency the expense of
placing data that would fail to meet accuracy criteria into
computer-readable form.
The National Geodetic Survey (NGS) has detennined
that the value to the national network of geodetic obser­
vations performed by other Federal, State, and local
organizations compensates for the costs of analyzing, adjust­
ing, and publishing the associated data. Consequently, a
procedure has been established for data from horizontal,
vertical, and gravity control surveys to be submitted to
NGS. Persons submitting data'-mtist adhere· to the require­
ments stated herein, but in any event, the filial decision of
acceptance on data will be the responsibility of the Chief,
NGs.·
The survey data must be submitted in the format speci­
fied in the Federal Geodetic Control Committee {FGCC)
publication, Input Formats and Specifications of the
National Geodetic Survey Data Base, which describes
�he procedures for submission of data for adjustment and
assimilation into the National Geodetic Survey .data base.
Volume I (Horizontal control data), volume II (Vertical
control data) or volume III (Gravity control data) may be
purchased from:
National Geodetic Information Branch (N/CG17x2)
National Oceanic and Atmospheric Administration
Rockville, MD 20852
Horizontal control surveys must be accomplished to at
least third-order, class I standards and tied to the National
Geodetic Horizontal Network. Vertical control surveys
must be accomplished in accordance with third-order or
higher standards and tied to the National Geodetic Verti-
* U.S. Government Printing Office : 1985 - 465-281/20664
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